Chapter 6 Lesson 9Probability and Predictionspgs. 310-314

What you’ll learn:Find the probability of simple eventsUse a sample to predict the actions of a larger group

Vocabulary

Outcomes (310): results of a probability problem

Simple Event (310): one outcome or a collection of outcomes

Probability (310): the chances of an event happening

Sample Space (311): the set of all possible outcomes

Theoretical Probability (311): what should occur

Experimental Probability (311): what actually occurs when conducting a probability experiment

Key Concept (310): Probability

Words: The probability of an event is a ratio that compares the number of favorable outcomes to the number

of possible outcomes.

Symbols: P(event) = number of favorable outcomes number of possible outcomes

The probability of an event is always between 0 and 1, inclusive.The closer a probability is to 1, the more likely it is to occur.

Example 1: Find Probability

Ten cards are numbered 1 through 10, and one card is chosen at random. Determine the probability of drawing an even number.

What we know: There are 10 cardsWe also know that 2,4,6,8,10 are even numbers.There are 10 possible outcomes: 1,2,3,4,5,6,7,8,9,10P(even) = number of favorable outcomes

number of possible outcomes P(even) = 5 = 1

10 2So the probability of drawing an even numberIs 1 or 50%. 2

In Example 1, the set of all possible outcomes is called the sample space.

What was the sample space for example 1?

{1,2,3,4,5,6,7,8,9,10} notice the sample space is in brackets

Example 2: Find Probability

1 2 3 4 5 6

1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Pg. 311

These are all the possible outcomes of rolling 2 dice, each with the numbers 1-6. This is the sample space.

Refer to the previous chartP(event) = Number of favorable outcomes Number of possible outcomes

Suppose two dice are rolled. Find the probability of rolling an odd sum.

Take a look at the sample space, add all the sums Ex. (1,2) = 3 and count how many are odd

There are 18 outcomes in which the sum is odd.

So, P(odd)= 18 = 1 = 50% 36 2

This means there is a 50% chance of rolling an odd sum.

The Probabilities in Example 1 & 2 are Theoretical Probability---what should happen

Example 3: Find Experimental Probability (what actually occurs)

Outcome Tally Frequency

Heads IIII IIII IIII 14

Tails IIII IIII I 11

This table shows the results of an experiment in which a coin wasTossed. Find the experimental probability of tossing a coin andgetting tails for this experiment.

Number of times tails occur = 11 = 11Number of possible outcomes 14+11 25

The experimentalProbability of gettingTails in this case is 11 25 or 44%

Example 4: Make a Prediction

Mary took a sample from a package of jellybeans and found that 30% of the beans were red. Suppose there are 250 jellybeans in the package. How many can she expect to be red?

The total number of jellybeans is 250, so 250 is the base. The percent is 30%.

You can choose to use the percent proportion or the percentequation. Let’s look at both ways.

Percent Proportion Way:

Mary took a sample from a package of jellybeans and found that 30% of the beans were red. Suppose there are 250 jellybeans in the package. How many can she expect to be red?

The total number of jellybeans is 250, so 250 is the base. The percent is 30%.

n = 30250 100

100n = 25030100n = 7500100n = 7500100 100 n = 75

So, Mary couldExpect 75 of the Jellybeans to be red.

Percent Equation Way:

Mary took a sample from a package of jellybeans and found that 30% of the beans were red. Suppose there are 250 jellybeans in the package. How many can she expect to be red?

The total number of jellybeans is 250, so 250 is the base. The percent is 30%.Part = Percent Base

n = .30(250)n = 75

So, as you can see that by usingEither formula, Mary couldExpect 75 of the jellybeans to beRed.

Your Turn!

There are 4 blue marbles, 6 red marbles, 3 green marbles, and 2 yellow marbles in a bag. Suppose you select one marble at random. Find the probability of each out come. Express each probability as a fractions and as a percent. Round to the nearest percent.

A. P(green)

B. P(red or yellow)

P(green) = 3 = 1 = 20% 15 5

P(red or yellow) = 8 ; 53% 15

Your Turn Again!

Suppose two number cubes are rolled. What is the probability of rolling a sum greater than 8?

Refer to the sample space on pg. 311.

10 = 5 ; about 28%36 18

A sample from a package of assorted cookies revealed That 20% of the cookies were sugar cookies. Suppose there are 45 cookies in the package. How many can be expected to be sugar cookies?

n = 20 n = .20(45)45 100 OR n = 9

n100 = 4520 Using either formula, you could 100n = 900 n = 9 expect 9 cookies to be sugar.

Quiz over 6-8 & 6-9 tomorrow!

We will be reviewing on Thursday and testing on Friday over Chapter 6.