1. Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 11 - Slide 1 P-10 Probability Binomial Probability Formula

2. Chapter 12 Section 11 - Slide 2 Copyright © 2009 Pearson Education, Inc. WHAT YOU WILL LEARN To solve problems which have two possible outcomes

3. Chapter 12 Section 11 - Slide 3 Copyright © 2009 Pearson Education, Inc. To Use the Binomial Probability Formula There are n repeated independent trials. Each trial has two possible outcomes, success and failure. For each trial, the probability of success (and failure) remains the same.

4. Chapter 12 Section 11 - Slide 4 Copyright © 2009 Pearson Education, Inc. Binomial Probability Formula The probability of obtaining exactly x successes, P(x), in n independent trials is given by: where p is the probability of success on a single trial and q (=1-p) is the probability of failure on a single trial.

5. Chapter 12 Section 11 - Slide 5 Copyright © 2009 Pearson Education, Inc. Example A basket contains 5 pens: one of each color red, blue, black, green and purple. Five pens are going to be selected with replacement from the basket. Find the probability that a.no blue pens are selected b.exactly 1 blue pen is selected c.exactly 2 blue pens are selected d.exactly 3 blue pens are selected

6. Chapter 12 Section 11 - Slide 6 Copyright © 2009 Pearson Education, Inc. Solution a. no blue pensb. exactly 1 blue pen

7. Chapter 12 Section 11 - Slide 7 Copyright © 2009 Pearson Education, Inc. Solution (continued) c. exactly 2 blue pensd. exactly 3 blue pens

8. Chapter 12 Section 11 - Slide 8 Copyright © 2009 Pearson Education, Inc. Example A manufacturer of lunch boxes knows that 0.7% of the lunch boxes are defective. a.Write the binomial probability formula that would be used to determine the probability that exactly x out of n lunch boxes produced are defective. b.Write the binomial probability formula that would be used to find the probability that exactly 4 lunch boxes out of 60 produced will be defective.

9. Chapter 12 Section 11 - Slide 9 Copyright © 2009 Pearson Education, Inc. Solution

10. Chapter 12 Section 11 - Slide 10 Copyright © 2009 Pearson Education, Inc. Example The probability that an egg selected at random has a weak shell and will crack is 0.2. Find the probability that a.none of 8 eggs selected at random has a weak shell. b.at least one of 8 eggs selected has a weak shell.

11. Chapter 12 Section 11 - Slide 11 Copyright © 2009 Pearson Education, Inc. Solution p = 0.2q = 1  0.2 = 0.8 a. We want 0 successes in 8 trials. b. at least 1 egg ≈ 1  0.167772 = 0.832228