copyright©ed2netlearning.inc1 review of probability

Copyright©Ed2NetLearning.Inc 1

REVIEW OF PROBABILITY


PREVIOUS KNOWLEDGE

1.1. Write Write 77 in simplest form 6363

2. Write 2. Write 5 5 x x 3 3 in simplest form 6 103. Write 4 x 2 in simplest form

7 3 4. Solve a = 5

6 15 5. Solve 8 = 28 y 42


THEORETICAL PROBABILITY


THEORETICAL PROBABILITY- DEFINITION

• The theoretical probability of an event is a ratio The theoretical probability of an event is a ratio that compares the number of favorable that compares the number of favorable outcomes to the number of possible outcomes.outcomes to the number of possible outcomes.

• P (event) = P (event) = number of favorable outcomes

number of possible outcomesnumber of possible outcomes

The probability that an event will occur is a The probability that an event will occur is a number from 0 to 1, including 0 and 1. The number from 0 to 1, including 0 and 1. The closer a probability is to 1, the more likely is it to closer a probability is to 1, the more likely is it to happen.happen.


Example – Find Probability

• In a spinner there are 8 equally likely outcomes In a spinner there are 8 equally likely outcomes – red, blue, green, yellow, orange, violet, white, – red, blue, green, yellow, orange, violet, white, black. Find the probability of spinning white.black. Find the probability of spinning white.

• P (white) = P (white) = number of favorable outcomes

number of possible outcomesnumber of possible outcomes

= = 1 1

8 8


Now your turn• A paper is cut into circular shapes and in that A paper is cut into circular shapes and in that

numbers from 1 – 10 is written. A number is numbers from 1 – 10 is written. A number is taken at random. Find the probability that the taken at random. Find the probability that the number chosen is i) 1 and ii) primenumber chosen is i) 1 and ii) prime


Complementary Events

• Complementary events are two events in which Complementary events are two events in which either one or the other must happen, but they either one or the other must happen, but they cannot happen at the same time. cannot happen at the same time.

• An example is a coin landing on heads or not An example is a coin landing on heads or not landing on heads. landing on heads.

• The sum of the probabilities of complementary The sum of the probabilities of complementary events is 1.events is 1.


Use Probability To Solve a Problem• In the television news hour it is reported that In the television news hour it is reported that

there is a 25% chance of raining. What is the there is a 25% chance of raining. What is the probability that it will not rain?probability that it will not rain?

• P ( rain) + P ( not raining) = 1P ( rain) + P ( not raining) = 1

0.25 + P ( not raining ) = 10.25 + P ( not raining ) = 1

P ( not raining ) = 1 – 0.25 = 0.75P ( not raining ) = 1 – 0.25 = 0.75

= = 75 75 = 75% = ¾ = 75% = ¾

100 100


Let’s try this!• A sports magazine predicted that Super Kings A sports magazine predicted that Super Kings

had a 30% chance of winning Golf had a 30% chance of winning Golf Championship. What is the probability that the Championship. What is the probability that the Super Kings will not win?Super Kings will not win?


OUTCOMES


OUTCOMES

• The set of all possible outcomes is called the The set of all possible outcomes is called the sample space. A tree diagram can also be used sample space. A tree diagram can also be used to show a sample space. When you make a tree to show a sample space. When you make a tree diagram, you have an organized list of diagram, you have an organized list of outcomes.outcomes.

• A tree diagram is a diagram that shows all A tree diagram is a diagram that shows all possible outcomes of an event.possible outcomes of an event.

• When you know the number of outcomes, you When you know the number of outcomes, you can easily find the probability that an event will can easily find the probability that an event will occur.occur.


Use a tree diagram to find probability• A car can be purchased with black or white colors. You may also A car can be purchased with black or white colors. You may also

choose leather, fabric or vinyl seats. Draw a tree diagram that choose leather, fabric or vinyl seats. Draw a tree diagram that shows all the buying options. What are the possible outcomes?shows all the buying options. What are the possible outcomes?

Car color Seats Outcomes

Black (B)

White (W)

Leather (L)

Fabric (F)

Vinyl (V)

BL

BF

BV

Leather (L)

Fabric (F)

Vinyl (V)

WL

WF

WV

The possible outcomes are 6


NOW YOUR TURN

• There are 2 spinners. In the 1There are 2 spinners. In the 1stst one, 2 colors – one, 2 colors – pink and grey are there and in the 2pink and grey are there and in the 2ndnd one, X, Y, one, X, Y, and Z are marked. Draw a tree diagram to show and Z are marked. Draw a tree diagram to show the sample space for the situation. How many the sample space for the situation. How many outcomes are possible? Find P ( pink, Y) ?outcomes are possible? Find P ( pink, Y) ?


STATISTICS: MAKING PREDICTIONS


What is Survey and Population

• A A surveysurvey is a method of collecting information. is a method of collecting information.• The group being studied is the The group being studied is the populationpopulation. .

Sometimes, the population is very large. To save Sometimes, the population is very large. To save time and money, part of the group called a time and money, part of the group called a samplesample, is surveyed., is surveyed.

• A good sample isA good sample is selected at random or without preference, representative of the population, and large enough to provide accurate data.


Determine a Good Sample• Example:Example: Every ninth person entering into a Every ninth person entering into a

market is asked to state whether his or her market is asked to state whether his or her favorite clothing shop. Determine whether the favorite clothing shop. Determine whether the sample is a good sample.sample is a good sample. The sample is good because asking every 9th

person ensures a random survey, the sample is large enough to provide accurate information.


Exercise • Every 4Every 4thth person entering into a public road is person entering into a public road is

asked whether he or she owns a pet. Determine asked whether he or she owns a pet. Determine whether the sample is a good sample.whether the sample is a good sample.


Let’s take a break!


Make predictions using proportions• Use the information in the table, what is the

probability that a student at the school ride a bike to school.

• P ( ride bike) = number of students that ride a bike number of students surveyed

P ( ride bike) = 10 = ¼ 40 Q. There are 400 students at the school. Predict how

many students would prefer bike to school.¼ = s 4001 x 400 = 4s

s =400 = 100 4

100 students prefer bike to school.

School School TransportationTransportation

MethodMethod StudentsStudents

WalkWalk 1010

Ride Ride bikebike

1010

Ride Ride busbus

1515

Get rideGet ride 55


NOW YOUR TURN

• A random sample of 40 A random sample of 40 flower shop customers flower shop customers was surveyed to find was surveyed to find customer’s favorite customer’s favorite flowers. The table shows flowers. The table shows the results. The shop the results. The shop expects to sell 50 expects to sell 50 bunches of flowers. How bunches of flowers. How many bunches of each many bunches of each flower should the shop flower should the shop order?order?

TypesTypes ShoppersShoppers

DaisyDaisy 88

SunflowerSunflower 44

RoseRose 2020

TulipsTulips 88


PROBABILITY AND AREA


Probability And Area

• The probability of landing in a specific region of a The probability of landing in a specific region of a target is the ratio of the area of the specific target is the ratio of the area of the specific region to the area of the target.region to the area of the target.

• P (specific region) = P (specific region) = area of specific region area of specific region

area of targetarea of target


Probability & Area

• Area of the whole region = l x w = 3 x Area of the whole region = l x w = 3 x 4 = 124 = 12

Area of the shaded region = 3 x 1 = 3Area of the shaded region = 3 x 1 = 3• P ( specific region) = P ( specific region) = 3 3 = 1/4 = 1/4

1212

• Find the probability that a randomly thrown dart will land Find the probability that a randomly thrown dart will land in the shaded region of each dartboard.in the shaded region of each dartboard.

If the dart is thrown 40 times, how many times would you expect to land it on the shaded region?

¼ = n/40

4n = 40 ; n = 40 = 10. So 10 times it will land on the shaded region.

4


Now your turn

• Find the probability that a randomly thrown dart will land Find the probability that a randomly thrown dart will land in the shaded region of each dartboard.in the shaded region of each dartboard.

3in3in

3 in

5 in

5 in


Let’s solve

• Suppose you threw a dart 200 times at the dartboard Suppose you threw a dart 200 times at the dartboard shown here. How many times would you expect it to land shown here. How many times would you expect it to land in the shaded regionin the shaded region

3in3in

3 in

5 in

5 in


Probability of Independent Events

• Two or more events in which the outcome of one Two or more events in which the outcome of one event does not affect the outcome of the other event does not affect the outcome of the other event are event are independent eventsindependent events.. The outcome of rolling a number cube does

not affect the outcome of choosing a marble from a bag.

• The probability of two independent events is The probability of two independent events is found by multiplying the probability of the first found by multiplying the probability of the first event by the probability of the second event.event by the probability of the second event.


Probability of Independent Events

• Example: Example: A coin is tossed, and A coin is tossed, and the spinner shown is spun. Find the spinner shown is spun. Find the probability of tossing heads the probability of tossing heads and spinning a 3.and spinning a 3. P(heads) = ½ P(3)=1/4 P(heads and 3) = ½ x ¼ or

1/8 So, the probability is 1/8,

0.125 or 12.5%


Your Turn!

• P(tails and even)P(tails and even)


Assessment sheet Alphonse asked every 4Alphonse asked every 4thth sixth grade student who walked sixth grade student who walked into a school dance to name their favorite sport.into a school dance to name their favorite sport.

football – 52; soccer – 22; baseball – 16; hockey - 10football – 52; soccer – 22; baseball – 16; hockey - 10

1.1. Find the probability a student prefers football?Find the probability a student prefers football?

2. If there are 375 students in the 62. If there are 375 students in the 6thth grade, how many can grade, how many can be expected to prefer football? be expected to prefer football?

3. Find the probability that a randomly thrown dart will land in 3. Find the probability that a randomly thrown dart will land in the shaded region of the dartboard. the shaded region of the dartboard.

3 mm

10 mm

14 mm


Assessment Sheet4. Suppose 60% of kids like video games. Predict the 4. Suppose 60% of kids like video games. Predict the

number of kids that prefer video game out of a group of number of kids that prefer video game out of a group of 200 kids? 200 kids?

5. How many different jeans and shirt combinations can be 5. How many different jeans and shirt combinations can be made with blue jeans and black jeans, and a white shirt, made with blue jeans and black jeans, and a white shirt, a blue shirt and a yellow shirt?a blue shirt and a yellow shirt?

6. The probability of a die landing on 6 is 1/6. The 1 in the 6. The probability of a die landing on 6 is 1/6. The 1 in the numerator stands for the number of ways that a die numerator stands for the number of ways that a die lands on 6. what does 6 stands for? lands on 6. what does 6 stands for?


Assessment Sheet

7.7. If a dart is thrown at the dartboard If a dart is thrown at the dartboard shown, what is the probability that it will shown, what is the probability that it will hit the region C? hit the region C?

8.8. What is the probability that a dart will What is the probability that a dart will land within the large square but outside land within the large square but outside the small square? the small square?

9.9. The probability that it will rain on The probability that it will rain on Saturday is 65%. The probability that it Saturday is 65%. The probability that it will rain on Sunday is 40%. What is the will rain on Sunday is 40%. What is the probability that it will rain on both days? probability that it will rain on both days?

10.10. Out of 50 students, 14 are interested in Out of 50 students, 14 are interested in publishing a school news paper. What publishing a school news paper. What is the probability that a student at this is the probability that a student at this school would be interested in publishing school would be interested in publishing a school news paper? 7/25a school news paper? 7/25

BB BB CC

CC BB CC

AA BB CC

12 CM 12 CM

4cm


Review • The theoretical probability of an event is a ratio that compares the number

of favorable outcomes to the number of possible outcomes.• P (event) = number of favorable outcomes number of possible outcomes• The set of all possible outcomes is called the sample space. A tree diagram

can also be used to show a sample space. When you make a tree diagram, you have an organized list of outcomes.

• A survey is a method of collecting information. The group being studied is the population. Sometimes, the population is very large. Part of the group called a sample is surveyed.

• A good sample is selected at random or without preference, representative of the population, and large enough to provide accurate data.

• The probability of landing in a specific region of a target is the ratio of the The probability of landing in a specific region of a target is the ratio of the area of the specific region to the area of the target.area of the specific region to the area of the target.

• The probability of two independent events is found by multiplying the The probability of two independent events is found by multiplying the probability of the first event by the probability of the second event.probability of the first event by the probability of the second event.


Great Job!

• Remember to do the practice worksheets!!Remember to do the practice worksheets!!

copyright©ed2netlearning.inc1 review of probability

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