Independent Events

Lesson 11-7Lesson 11-7Pg. # 432-433Pg. # 432-433

CA Content StandardsStatistics, Data Analysis, and Probability 3.4:

I understand that the probability of one event following another, in independent trials, is the product of the two probabilities.

Number Sense 2.1:I solve problems involving multiplication of positive fractions.

Statistics, Data Analysis, and Probability 3.3***:I represent probabilities as ratios and percentages between 0

and 100 and verify that the probabilities computed are reasonable; I know that if P is the probability of an event, 1-P is the probability of an event not happening.

Vocabulary: COMPOUND EVENT

An event that is a combination of two or more single events.

Vocabulary: INDEPENDENT EVENTSTwo events in which the outcome of the second is not affected by the outcome of the first.

Objective

Find the probability that two independent events will occur.

Math Link: You know how to find the probability that an event will occur. Now you will learn how to find the probability that two events will occur.

Example 1. Find each probability.

P (red or purple)

P (not red or purple)

Which is greater: P (red or green) or P (not red or green)?

Please note…

We just rehearsed probabilities involving one event OR another event (addition); this lesson will focus on probabilities involving one event AND another event (multiplication).

Example 2. The school carnival has a spinner game. You can win a prize by spinning an A on the first spinner and then yellow on the second spinner. What is the probability of winning a prize?

A

C

B

A Little Background…Spinning both spinners is a compound event. A compound event is a combination of two or more simple events.

The outcome of the first spinner does not influence the outcome of the second spinner. The two spins are independent events.

To find P (A, yellow), find the probability of each event and multiply.

Step 1. Find each probability.P (A) = 1/3 P (yellow) = 2/4 = 1/2

Step 2. Multiply.1/3 x 1/2 = 1/6

The probability of winning a prize is 1/6, or 1 out of 6 tries.

Example 3. What is the probability of NOT winning a prize in the spinner game in Example 2?

P (not winning) = 1 - P (winning)

= 1 - 1/6

= 5/6

The probability of not winning is 5/6, or 5 out of 6 tries.

The letters of the word FLORES were placed in a bag; find the probability of forming the word OR if the first letter is put back before picking the second letter.

Step 1. Find each probability.P (O) = 1/6 P (R) = 1/6

Step 2. Multiply.1/6 x 1/6 = 1/36

Example 4.

The letters of the word FLORES were placed in a bag; find the P (L, E) if the first letter is NOT put back before picking the second letter.

Step 1. Find each probability.P (L- First draw) = 1/6 P (E- Second draw) =

1/5

Step 2. Multiply.1/6 x 1/5 = 1/30

Example 5.

Moral of the Story

To find the probability of two independent events, find the probability of each event and multiply.