1

Unit 12 Probability

NAME:______________________

TEACHER:____________________

GRADE:______________________

0 1 2

1 4

1 4

3

Impossible Certain Equal Chance

Somewhat

Likely Very Likely

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Outcomes Classwork Day 1

Important Vocabulary:

Outcomes:________________________________________________________________________________

Sample Space: _____________________________________________________________________________

Fundamental Counting Principle:_______________________________________________________________

Example: Complete the tree diagram for tossing a coin three times.

a) P(HHH) = b) P(TTT) =

c) P(at least one H) = d) P(exactly 2 T’s) =

e) If you tossed 4 coins, how many possible outcomes would there

be?

Tree Diagrams: Displays all outcomes in detail

Make a tree diagram to represent the sample space of flipping a balanced coin and rolling a fair die.

Total Outcomes:_______

What is the probability of the coin landing on tails and rolling an even number?

A pizza shop offers the following options for a slice of pizza: 1. TYPE: Regular or Sicilian

2. CRUST: Thin or Thick 3. TOPPINGS: Pepperoni, Sausage, Meatball, or Anchovies

Make a tree diagram to represent the sample space of the various slices that could be made.

Total Outcomes:_______

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Outcomes Classwork Day 1

Fundamental Counting Principle (FCP): Allows us to determine the number of outcomes in a sample space

by multiplying the number of ways each event can occur.

Examples:

A pizza shop offers the following options for a slice of pizza:

TYPE: Regular or Sicilian

CRUST: Thin or Thick

TOPPINGS: Pepperoni, Sausage, Meatball, or Anchovies

Use the FCP to determine the total number of possible slices of pizza.

1. A restaurant has four different appetizers, three different entrees, and two different desserts on their price-

fixed menu. How many different outcomes can there possibly be?

2. If Mr. DeMeo has fifteen pairs of pants, twenty-three collared-shirts, and sixty-four ties; what are the total

number of outfits that he can possibly create?

3. If a student rolls two dice, what is the number of total outcomes?

4. Find the total number of different outfits that can be made from the following:

3 different sweaters, 4 turtlenecks, and 2 pairs of jeans.

5. When rolling a fair die and flipping a balanced coin, what is the total possible outcomes?

6. Two friends meet at a grocery store and remark that a neighboring family just welcomed their second child.

It turns out that both children in this family are girls, and they are not twins. One of the friends is curious about

what the chances are of having 2 girls in a family's first 2 births. Suppose that for each birth the probability of a

“boy” birth is 0.5 and the probability of a “girl” birth is also 0.5.

Draw a tree diagram demonstrating the four possible birth outcomes for a family with 2 children (no twins).

Use the symbol “B” for the outcome of “boy” and “G” for the outcome of “girl.” Consider the first birth to be

the “first stage.”

What is the probability of a family having 2 girls in this situation? Is that greater than or less than the

probability of having exactly 1 girl in 2 births?

B (0.5)

G (0.5)

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Outcomes Homework Day 1

1. Create a tree diagram and list the sample space representing all possible outcomes of flipping a coin twice.

(Complete the tree and list the probabilities)

2. Create a tree diagram and list the sample space representing all possible outcomes of rolling a fair die twice.

3. Create a tree diagram and list the sample space representing all possible outcomes of choosing a hat that

comes in black, red, or white AND medium or large.

4. Create a tree diagram and list the sample space representing all possible outcomes of choosing peach or

vanilla yogurt topped with peanuts, chocolate, strawberries, or granola.

5. At a wedding you can choose from 4 different meats (lobster, steak, chicken, or pork). You can choose from

2 side dishes (pasta or vegetables) and from 2 desserts (fruit or ice cream). How many total outcomes are

possible? Use the FCP.

6. At dinner you have the choice of 3 different soups, 4 appetizers, 5 main meals, and 3 desserts. Find the

number of possible outcomes of choosing 1 of each course from the menu.

H (0.5)

T ( ) T (0.5)

H (0.5) H H (0.5)(0.5) = 0.25

T (0.5)

H (0.5)

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Simple Events/Theoretical Classwork Day 2

Important Vocabulary:

Probability: The chance that some event will happen; the ratio of ways a specific event can happen to the total

number of outcomes.

𝑃(𝑒𝑣𝑒𝑛𝑡) =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑜𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡

𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠

Relative Frequency- the ratio of the number of observations in a statistical category to the total number of

observations.

*Probability can be expressed as a fraction, a decimal, or a percentage.*

Complementary Events: the set of all outcomes in the sample space that are not included in the event. Example:

Rolling a 3 on a number cube is 1/6 the complement is 5/6 ( numbers 1, 2, 4, 5, 6)

P(event) + P(complement) = 1

Examples:

1. A fair coin is flipped, what is the probability of getting a ‘tails’?

Percent___________ Fraction___________ Decimal__________

2. The probability that it rains today is 60%. What is the probability that it does not rain?

Percent___________ Fraction___________ Decimal__________

3. A spinner consists of six equal sections numbered 1-6.

What is the probability of the spinner landing on 5?

a) Find P(3). b) What is the probability of getting an even number?

c) What is P(3 or 4)? d) What is the probability of the spinner landing on 7?

4. John has eight red marbles and four blue marbles in a jar. What is the probability that John picks a marble at

random, and it is not red?

Answer the following questions to demonstrate knowledge of probability:

5. What is the sum of the probabilities of all the outcomes in a sample space?

6. The probability of a certain event occurring is 1

4 .

Express this probability as a decimal. Express this probability as a percentage.

What is the probability that this event does not occur?

Simple Events/Theoretical Classwork Day 2

6

7. Which of these cannot be considered a probability of an outcome? Explain.

[a] 1

3 [b] -0.59 [c] 1 [d] −

1

5 [e] 0

[f] 1

2 [g] 0.80 [h] 1.45 [i] 112% [j] 100%

4

1

2

1

4

3

Describe each event as impossible, likely, unlikely, or certain.

8. The probability of tossing a number cube and getting 5 is 6

1. _________________

9. The probability of spinning blue on a spinner is 0. ___________________________

10. The probability of selecting a red marble from a bag of marbles is 0.47. ____________________

11. The probability of selecting a tile with a vowel on it from a box of tiles is 20

3. ________________

12. If a fair die is rolled one time, find the probability of the following outcomes:

[a] rolling a four

[b] rolling an even number

[c] rolling a number greater than four

[d] rolling a number less than seven

Which was most likely to occur (a, b, c or d)?

13. A box contains 5 green pens, 3 blue pens, 8 black pens, and 4 red pens. One pen is picked at random.

[a] What is the probability the pen is green?

[b] What is the probability the pen is blue or red?

[c] What is the probability the pen is gold?

14. The spinner is used for a game. Write each probability as a fraction.

[a] P(3) [b] P(5) [c] P(1 or 2) [d] P(odd) [e] P(a number at most 2)

2 1

3 4

1

Impossible Certain Equal Chance unlikely likely 0

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Simple Events Classwork Day 2

15. A spinner has eight congruent sections, which are colored in the following way:

[i] 2 Red Sections

[ii] 2 Yellow Sections

[iii] 1 Blue Section

[iv] 3 Green Sections

What is the probability of the following outcomes:

[a] Spinning a Red b] Spinning a Red or a Green [d] Not Spinning a Color in the American Flag

*Example 16 Below are three different spinners. If you pick green for your color, which spinner would give

you the best chance to win? Give a reason for your answer.

Spinner A

Green Red

Spinner B

Red

Green

Spinner C

Red

Green

DECK OF PLAYING CARDS

I. 52 TOTAL CARDS (FOUR SUITS OF EACH - ♥ ♦ ♣ ♠)

a. FACE CARDS (JACK, QUEEN, KING)

b. OTHER CARDS (2-10, AND ACE)

18. If a magician asks you to select one card from a fair deck of cards, find:

[a] P(ace) [b] P(red) [c] P(not a diamond) [d] P(Queen of spades)

[e] Probability of selecting a Spade or a Diamond [f]Probability of selecting a red picture card

[g] Probability of selecting a 1

19. A weather forecast states that there is an 80% probability of rain tomorrow. Which term best describes the

likelihood of rain tomorrow?

A. Impossible B. Unlikely C. Likely D. Certain

4 SUITS

a. SPADES (BLACK)

i. 13 TOTAL SPADES ♠ (2-10, J, Q, K, A)

b. CLUBS (BLACK)

i. 13 TOTAL CLUBS ♣ (2-10, J, Q, K, A)

c. HEARTS (RED)

i. 13 TOTAL HEARTS ♥ (2-10, J, Q, K, A)

d. DIAMONDS (RED)

i. 13 TOTAL DIAMONDS ♦ (2-10, J, Q, K, A)

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Simple Events Homework Day 2(2 pages)

1. A spinner with six equal sections is used for a game. The sections are numbered 1-6 Write each probability

as a fraction.

P(3) b. P(7) c. P(3 or 4) d. P(even) e. P(not 5)

2. A bag contains 4 red marbles, 3 orange marbles, 7 green marbles, and 6 blue marbles. Express each

probability as a fraction:

P(red) b. P(green) c. P(red or blue) d. P(not green) e. P(purple)

3. If the probability that it will snow tomorrow is 0.85, what is the probability that it will not snow tomorrow?

4. There is a 30% chance that it will rain on Saturday. What is the probability that it will not rain?

#’s 5 – 6 Describe each event as impossible, likely, equal chance, unlikely, or certain.

5. The probability of a spinner landing on a shaded section is 53%.

6. The probability of tossing a number cube and rolling a number greater than 1 is 6

5.

7. A company that manufactures light bulbs finds that one out of every twenty light bulbs are defective.

a) Express, as a fraction, the probability that a random light bulb is defective. (defective-broken)

b) Express, as a fraction, the probability that a random light bulb is not defective.

c) In a sample of 100 light bulbs, how many bulbs should the company expect to be defective?

d) The manager of your branch of the company tells you that 20% of the light bulbs manufactured are

defective. Is this an accurate statement?

16. There are 4 aces and 4 kings in a standard deck of 52 cards. You pick one card at random. What is the

probability of selecting an ace or a king? Explain your reasoning.

______________________________________________________________________________________________ ______________________________________________________________________________________________

17. Reasoning: A box contains 150 black pens and 50 red pens. Chris said the sum of the probability that a

randomly selected pen will not be black and the probability that the pen will not be red is 1. Explain whether

you agree. ______________________________________________________________________________________________

_______________________________________________________________________________Next Page

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1 1/2 0

Probability Scale

Impossible Unlikely Equally Likely to

Occur or Not OccurLikely Certain

Example 18 Decide where each event would be located on the scale above. Place the letter for each event on

the appropriate place on the probability scale.

Event:

A. You will see a live dinosaur on the way home from school today.

B. A solid rock dropped in the water will sink.

C. A round disk with one side red and the other side yellow will land yellow side up when flipped.

D. A spinner with four equal parts numbered 1-4 will land on the 4 on the next spin.

E. Your name will be drawn when a name is selected randomly from a bag containing the names of all of

the students in your class.

F. A red cube will be drawn when a cube is selected from a bag that has five blue cubes and five red cubes.

G. The temperature outside tomorrow will be -250 degrees.

Example 19. Design a spinner so that the probability of green is 1.

Example 20 Design a spinner so that the probability of green is 0.

Example 21 Design a spinner with two outcomes in which it is equally likely to land on the red and green parts.

______________________________________________________________________________________________ Mixed Review 22. Simplify: 3(2x – 3) – 10(x – 2) 23. -2x and 2x are additive inverses because…. 24. Solve: 3x – 5x = 4 25. Solve: 3x > -9 26. Solve: -3x > -9

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Independent Events Classwork Day 3

Important Vocabulary:

Compound Event: _________________________________________________________________________

Independent Event: ________________________________________________________________________

Dependent Event: _________________________________________________________________________

Each fraction is the theoretical probability of an event.

When all the possible outcomes of an experiment are equally likely, the probability of each outcome is

𝑃(𝑜𝑢𝑡𝑐𝑜𝑚𝑒) =1

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠.

Determine if each of the following events are considered independent or dependent:

[a] Tossing a coin and drawing a card from a deck.

[b] Drawing a marble from a jar, not replacing it, and then drawing a second marble.

[c] Driving on ice and having an accident.

[d] Having a large shoe size and having a high IQ

[e] Not studying for a test and receiving a low test score.

[f] Picking a card from a deck, replacing it, and choosing another card.

[g] Picking a card from a deck, and then choosing another card without replacing the first.

[h] Picking a marble from a jar, replacing it and picking another marble.

[i] Committing a crime and getting arrested.

TO FIND THE PROBABILITY OF COMPOUND INDEPENDENT EVENTS, MULTIPLY THE

PROBABILITY OF EACH EVENT.

𝑷(𝑨 𝒂𝒏𝒅 𝑩) = 𝑷(𝑨) × 𝑷(𝑩)

Examples 1:

When flipping a coin twice, what is the probability of getting two tails?

Example 2: A game calls for the player to flip a coin and then roll a fair die. Find each probability:

[a] P(tails and 4) [b] P(heads and odd) [c] P(tails and 7)

Independent Events Classwork Day 3 Practice:

When one is the numerator it means each event has

an equal chance.

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1. A person draws a card from a deck of cards, puts the card back and picks again. Find the following

probabilities:

[a] P(red and red) [b] P(5 of clubs and 7 of spades)

[c] P(two face cards) [d] P(two spades)

2. There are 4 green marbles, 5 red marbles, 9 blue marbles, and 2 orange marbles in a jar. One marble is

selected at random, replaced, and another is selected. Find the following probabilities.

[a] P(green and blue) [b] P(red and orange) [c] P(red and yellow)

[d] P(two blue marbles) [e] P(no red marbles) [f] P(red or blue, and green)

3) An arrangement of 8 students is shown. The numbers of all the students are in a basket. The teacher selects

a number and replaces it. Then the teacher selects a second number. Find each probability.

a) P(student 1, then student 8) =

b) P(student in row A, then student in row B) =

c) P(student in row A, then student 6, 7, or 8) =

Row Student

A 1 2 3 4

B 5 6 7 8

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1 2 3 4

1 (1,1) (1,2) (1,3) (1,4)

2 (2,1) (2,2) (2,3) (2,4)

3 (3,1) (3,2)) (3,3) (3,4)

4 (4,1) (4,2) (4,3) (4,4)

Independent Events Homework Day 3

1. A spinner has eight equal sections numbered 1-8. The spinner is spun twice. Find the following

probabilities:

[a] P(1 and 2) [b] P(3 and 3) [c] P(odd and even) [d] P(1 and not 1)

[e] P(7 and 0) [f] P(1 and 0) [g] P(not 0 and not 7) [e] P(both numbers < 4)

2. A company produces two different sized light bulbs. One out of every 25 big bulbs is defective. One out of

every 50 small bulbs is defective.

a) What is the probability that when purchasing one of each, both will be defective?

b) What is the probability that when purchasing only one small bulb, the bulb will not be defective?

c) In a sample of 200 big bulbs, how many defective bulbs are to be expected?

d) In a sample of 200 small bulbs, how many defective bulbs are to be expected?

3. What is the probability of flipping a coin 3 times and getting heads every time?

4. What is the probability of getting five consecutive tails when flipping a coin five times?

5. A spinner has four equal sections numbered 1 though 4. You spin it twice. Use the sample space below to

find each probability. Second Spin

a) P(1,2) b) P(1,odd) c) P(even, odd)

Firs

t Sp

in

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DEPENDENT EVENTS CLASSWORK DAY 4

To find the probability of compound dependent events, multiply the probability of the first event and the

probability of the second event after the first event happens. (Remember- “Probability Land”- you get to

pick one at a time but you get what you want)

𝑷(𝑨 𝒂𝒏𝒅 𝑩) = 𝑷(𝑨) × 𝑷(𝑩 𝒂𝒇𝒕𝒆𝒓 𝑨) Describe in your own words the phrase “without replacement”.

____________________________________________________________________________________

Example:

There are 4 green marbles, 5 red marbles, 9 blue marbles, and 2 orange marbles in a jar. One marble is selected

at random, and then another is selected without replacement.

a) Find the probability that two blue marbles will be selected

Step 1 : Find the probability of the first event happening:

P(first marble is blue) =

Step 2: Find the probability of the second event happening, assuming the first event did happen:

P(second marble is blue) =

Step 3: Multiply the probabilities of each event:

P(two blue marbles) =

b) Find the probability that the first marble will be red and the second will be green:

P(Red and then Green) =

1. A mason jar contains eighteen marbles in the following colors:

[i] 6 green marbles

[ii] 4 blue marbles

[iii] 7 red marbles

[iv] 1 black marble

What is the probability of the following outcomes without replacement?

[a] P(green and then blue) [b] P(two reds) [c] P(black and then black)

[d] P(two blacks) [e] P(red and then green) [f] P(black and then not black)

[g] P(green and then not red) [h] P(two blues)

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DEPENDENT EVENTS CLASSWORK DAY 4

2. Five girls and seven boys want to be the two broadcasters for a school show. To be fair, a teacher puts their

names in a hat and selects two. Find P(girl, then boy).

Make a Plan: The selections of the two names are (dependent or independent) events? Find the probability of

selecting girl first. Then find the probability of selecting a boy after selecting a girl.

Carry out the Plan: P(girl first) = P(boy after girl) =

Final answer: P (girl, then boy) =

3. A student writes the numbers (1-9) on index cards, and then places them in a hat. If another student draws

two cards without replacing them, what is the probability of:

[a] P(8 and then 5) [b] P(both digits being even)

[c] P(both digits being odd) [d] P(both digits being perfect squares)

[e] P(1 and then 2) [f] P(9 and then a number less than 9)

[g] P(both numbers greater than 5) [h] P(both numbers are prime)

Easy Medium Challenging

4. You select the letter A from the group. Without replacing the A, you select a second letter. Find each probability. a) P(Z) = b) P(grey) = c) P(consonant) = d) P(vowel) =

5. A box contains 20 cards numbered 1-20. You select a card. Without replacing the first card, you select a second card. Find each probability. a) P(1, then 20) = b) P(3, then even) = c) P(even, then 7) =

6. The face cards are removed from a standard deck of 52 cards, and the rest are set aside. Two cards are drawn at random from the face cards. Once a card is selected, it is not replaced. Find each probability. a) P(2 queens) = b) (black jack and then red queen) = c) P(black jack and then black card) =

A G B L

O K Z E

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DEPENDENT EVENTS HOMEWORK DAY 4

1. Mr. DeMeo has to select two students from class to join the SLAM. He decides to choose randomly from a

class of eleven girls and nine boys.

[a] What is the probability that he will choose a girl first and then a boy second?

[b] What is the probability he will choose a boy first and then a girl second?

2. There were 5 cards in a bag labeled 0 through 4. Find each probability if two cards are picked with no

replacement. (Write the numbers down to help you)

[a] P(2 and then 4) [b] P(2 and then 2) [c] P(1 and then 2 and then 3)

[d] P(prime # and then 0) [e] P(three 0’s) [f] P(# less than 2 and then a 4)

3. In a standard deck of cards: (There are 52 cards in a deck) (4 of each kind) (13 of each suite: ♥♦♣♠) [a] What is the probability of picking a king or a queen?

[b] What is the probability of picking a king and then a queen with replacement?

[c] What is the probability of picking a king and then a queen without replacement?

[d] What is the probability of picking four consecutive aces without replacement?

Review

4. In a board game, you randomly select one number card and one category card. The possible numbers are 1,2

and 3. The possible categories are Science, History, Sports, Language, and Math. Assume that each outcome is

equally likely. Make a tree diagram and sample space to display the outcomes. (*Separate Paper please-This

may be collected)

5. William can spend no more than $15 at a carnival. The entrance fee to the carnival is $7, and rides cost $2

each. Which inequality best represents the number of rides r that William can afford?

a) r ≤ 4 b) r < 4 c) r ≤ 11 d) r < 11

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EXPERIMENTAL PROBABILITY CLASSWORK DAY 5

IMPORTANT VOCABULARY:

Theoretical Probability:____________________________________________________________________

Empirical (Experimental) Probability:_____________________________________________________________

When you were spinning the spinner and recording the outcomes, you were performing a chance experiment.

You can use the results from a chance experiment to estimate the probability of an event.

THEORETICAL EXAMPLE: What should happen.

1. A fair coin is flipped four times.

[a] P( first flip will be heads) [b] P( all four flips will be tails)

[c] If you were to flip the coin a total of 100 times, how many times would you expect heads to appear?

EMPIRICAL(EXPERIMENTAL)EX.: BASED ON OBSERVED DATA-What actually did happen.

Class Activity: Example 2: The experiment requires a brown paper bag that contains 10 yellow, 10 green, 10

red, and 10 blue cubes. The cubes are identical except for their color. Your teacher will conduct a chance

experiment. Twenty cubes are drawn at random and replaced. After each cube is drawn, have students record

the outcome in the table.

Theoretically, what should happen? A) P(yellow) B) P(green) C) P(red) D P(blue)

a) Based on the 20 trials, estimate for the probability of

a. choosing a yellow cube. b. choosing a green cube. c. choosing a red cube. d. choosing a blue cube.

b) If there are 40 cubes in the bag, how many cubes of each color are in the bag? Explain.

c) If your teacher were to randomly draw another 20 cubes one at a time and with replacement from the bag,

would you see exactly the same results? Explain.

Trial Outcome

1

2

3

4

5

6

7

8

9

10

Trial Outcome

11

12

13

14

15

16

17

18

19

20

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3. A probability experiment is conducted. In the experiment, a BALANCED coin is flipped 20 times. The

results are displayed in the graph below:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 T

H X X X X X X X X X X X X 12

T X X X X X X X X 8

[a] What is the EMPIRICAL, EXPERIMENTAL, probability of flipping heads?

[b] What is the EMPIRICAL, experimental, probability of flipping tails?

[c] How could you make this experiment more representational of the theoretical probability?

(How can this be more accurate?)

[d] According to this experiment, how many times would you expect to get heads in 300 flips?

Example 4 Jenna’s husband, Rick, is concerned about his diet. On any given day, he eats 0, 1,2,3, or 4 servings

of fruit and vegetables. The probabilities are given in the table below.

Number of Servings of Fruit and Vegetables 0 1 2 3 4

Probability 0.08 0.13 0.28 0.39 0.12

On a given day, find the probability that Rick eats:

a. Two servings of fruit and vegetables.

b. More than two servings of fruit and vegetables.

c. At least two servings of fruit and vegetables.

d. Find the probability that Rick does not eat exactly two servings of fruit and vegetables.

The diagram below shows a spinner designed like the face of a clock. The sectors of the spinner are colored red

(R), blue (B), green (G), and yellow (Y).

Spin the pointer, and award the player a prize according to the color on which the pointer stops.

Writing your answers as fractions in lowest terms, find the probability that the pointer stops on:

a. red: b. blue: c. green: d. yellow:

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EXPERIMENTAL PROBABILITY CLASSWORK DAY 5

PRACTICE:

1. A probability experiment is conducted to find the experimental probability of getting various sums when two

number cubes are rolled. The results of 50 rolls are shown below:

[a] According to the experiment, what is the experimental probability of rolling a sum of 9?

[b] What is the experimental probability of rolling a sum of 8?

[c] What is the experimental probability of rolling a sum that is greater than 7?

[d] What is the experimental probability of rolling a sum that is greater than or equal to 7?

[e] Which sum is most likely to appear based on the experiment?

[f] Which sums are least likely to appear?

[g] In this experiment, two number cubes were rolled. What is the theoretical probability of getting two 3s? Is

this the only way to get a sum of 6?

[h] Why is it that certain sums are more likely to appear than others?

[i] Why is it impossible to roll a 1?

Sum

# of

rolls

0

2

4

6

8

10

12

2 3 4 5 6 7 8 9 10 11 12

Results

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EXPERIMENTAL PROBABILITY HOMEWORK DAY 5 (1 OF 2 PAGES)

1. When tossing a coin, what is the theoretical probability of:

a) P (heads) b) P(tails) c) P(heads or tails)

2. Perform your own experiment (get a coin). Flip a coin 50 times. Record the results.

Tally Total

Heads

Tails

Use your data to find the experimental probability of:

a) P (heads) b) P(tails) c) P(heads or tails)

3. Write a conclusion comparing the results from your experiment and the theoretical probability.

4. How many heads would you expect when flipping a fair balanced coin fifty times?

5. How many primes would you expect when rolling a fair die one hundred times?

6. How many times would you expect to pick a diamond, if you selected a card from a fair deck thirty-two

times?

7. How many times would you expect to roll a 5 when rolling a fair die twelve times?

8. The odds of a particular team to win the Super Bowl are 1/8. If these odds stayed consistent every year, how

many super bowl titles would you expect this team to have in the next 80 years?

9. A fair die is rolled twice.

How many possible outcomes are there?

What is the probability of rolling a 3 and then a 5? GO TO NEXT PAGE

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EXPERIMENTAL PROBABILITY HOMEWORK DAY 5

10. A company that produces car parts tests a sample of fifty parts. After testing all fifty parts, they find that 7

parts are defective.

[a] What is the experimental probability of a part being defective?

[b] What is the experimental probability of a part being functional?

[c] How many defective parts would you expect in a batch of 1000 parts?

[d] How could the company find a more accurate representation of their defective parts?

11. A particular game of chance is played by flipping a coin, rolling a fair die, and then picking a card from a

fair deck. What is the probability of winning the game if:

[a]Winning means (heads, one, ace) [b] Winning means (tails, odd, black)

Example 12 A seventh grade student surveyed students at her school. She asked them to name their favorite

pet. Below is a bar graph showing the results of the survey.

Favorite Pet

Fre

qu

en

cy

GerbilFishSnakeTurtleCatDog

10

9

8

7

6

5

4

3

2

1

0

Now suppose a student will be randomly selected and asked what his or her favorite pet is.

a. What is your estimate for the probability of that student saying that a dog is their favorite pet?

b. What is your estimate for the probability of that student saying that a gerbil is their favorite pet?

c. What is your estimate for the probability of that student saying that a frog is their favorite pet?

13. Which of the following shows a proportional relationship? a) y= x + 3 b) y = 3x c) d)

14. Mark has a total of 600 XBOX games. Of those games 1/3 is violent, out of the violent games 30% use bad

language, and out of those games (violent and bad language), 3/5 have are extremely inappropriate. How many

games were considered extremely inappropriate?

Y 13 12 9

X 5 4 3 Y 15 12 9

X 5 4 3

Use the results from the survey to answer

the following questions.

a. How many students answered the

survey question?

b. How many students said that a

snake was their favorite pet?

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Theoretical Predictions CLASSWORK Day 6

EXPERIMENTAL PROBABILITY: Determined by OBSERVING and COUNTING outcomes from a

sample. This is what ACTUALLY happens!

THEORETICAL PROBABILITY: Determined by what we EXPECT will happen.

Relative Frequency- the ratio of the number of observations in a statistical category to the total number of

observations.

The more data collected, the closer the estimates are likely to be to the actual probabilities. Guided Example:

How many times would you EXPECT to get a B if you spun the above spinner 4 times?

To get a B – your chances are4

1. So multiply the 4 times by

4

1 to get your answer of 1.

1. How many times would you EXPECT to get a D if you spun the spinner to the right:

a) 4 times b) 100 times c) 200 times d) 1,000 times

2. How many times would you EXPECT to get an A,B, or C if you spun the above spinner:

a) 4 times b) 52 times c) 64 times d) 100 times

Which letter will the spinner most likely land on? _______ Explain _____________________________

3. How many times would you EXPECT to get a 5 if you rolled the die:

a) 6 times b) 36 times c) 132 times d) 6,000 times

5) A company that produces car parts tests a sample of fifty parts. After testing all fifty parts, they find that 7

parts are defective.

a) What is the experimental probability of a part being defective?

b) How many defective parts would you expect in a batch of 1000 parts?

c) How could the company find a more accurate representation of their defective parts?

6) A school has 1,060 students. The results of a survey are shown.

Students Surveyed Students Who Produced Computer Art

40 24

If the trend in the table continues, which is the best prediction of the total number of students who produced

computer art?

A) 260 students B) 480 students C) 640 students D) 790 students

7) The quality control engineer of Top Notch Tool Company finds flaws in 8 of 60 wrenches examined.

Predict the number of flawed wrenches in a batch of 2,400.

A A

A

B

B

D

C

C

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Theoretical Predictions CLASSWORK Day 6

Example 8 Which of the following graphs would NOT represent the relative frequencies of heads when tossing

1 penny? Explain your answer. ________________________________________________________________

Part B Jerry indicated that after tossing a penny 30 times, the relative frequency of heads was 0.47 (to the

nearest hundredth). He indicated that after 31 times, the relative frequency of heads was 0.55. Are Jerry’s

summaries correct? Why or why not?

Part C Jerry observed 5 heads in 100 tosses of his coin. Do you think this was a fair coin? Why or why not?

Jerry and Michael played a game and you need to pick a Blue to win. The following results are from their

research using the same two bags:

Jerry’s research: Michael’s research:

Number of Red

chips picked

Number of Blue chips

picked

Number of Red

chips picked

Number of Blue chips

picked

Bag A 2 8 Bag A 28 12

Bag B 3 7 Bag B 22 18

1. If all you knew about the bags were the results of Jerry’s research, which bag would you select for the game?

Explain your answer. Using only Jerry’s research, the greater relative frequency of picking a blue chip would

be____________________________________________________________________________________________________ _____________________________________________________________________________________

2. If all you knew about the bags were the results of Michael’s research, which bag would you select for the

game? Explain your answer. Using Michael’s research, the greater relative frequency of picking a blue chip would

be_____________________________________________________________________________________________________ ________________________________________________________________

3. Does Jerry’s research or Michael’s research give you a better indication of the make-up of the blue and red

chips in each bag? Explain why you selected this research.______________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

Graph A Graph B

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Theoretical Predictions HOMEWORK Day 6

1) Find the experimental probability for Seneca Boys Basketball Team. P(loss) =

Wins: 22 Losses: 3

2) A quality control engineer at a factory inspected 300 glow sticks for quality. The engineer found 15

defective glow sticks. What is the experimental probability that a glow stick is defective? How many glow

sticks would the engineer expect to find defective out of 900?

3) A quality control inspector finds flaws in 6 of 45 tools examined. If the trend continues, what is the best

prediction of the number of defective tools in a batch of 540?

4) The population of Los Angeles, California, throughout the 20th century is shown in the table to the left.

Between which 2 years did the population increase the most?

Answer between ________________ and _______________________

Based on the data in the table, predict the population of Los Angeles in

the year 2020. Justify your prediction.

Review

5) During hockey practice, Dane blocked 19 out of 30 shots and Matt blocked 17 out of 24 shots. For the first game, the coach wants to choose the goalie with the greater probability of blocking a shot. Which player should he choose? ______________ Explain

6) After tax (8%), a Bose stereo system costs $5,400. Jim, the salesperson makes 5% commission on his sales.

How much commission did Jim earn on his sale?

7) A diver’s elevation is decreasing at a rate of 30 feet per minute. If the diver starts at sea level, what will her

elevation be after 2.5 minutes?

A. – 75 feet B. – 12 feet C. 12 feet D. 75 feet