2. Holt McDougal Algebra 2 Binomial Distributions How do we use the Binomial Theorem to expand a binomial raised to a power? How do we find binomial probabilities and test hypotheses?

3. Holt McDougal Algebra 2 Binomial Distributions 1 Understand the Problem 2 Make a Plan Solve 3 Look Back 4 Problem-Solving Application 4 Steps for Problem Solving

4. Holt McDougal Algebra 2 Binomial Distributions Example 1: Problem-Solving Application You make 4 trips to a drawbridge. There is a 1 in 5 chance that the drawbridge will be raised when you arrive. What is the probability that the bridge will be down for at least 3 of your trips? 1 Understand the Problem The answer will be the probability that the bridge is down at least 3 times. The probability that the drawbridge will be down is = 0.8. List the important information: You make 4 trips to the drawbridge. 1 in 5 chance will be raised probability that the bridge will be down

5. Holt McDougal Algebra 2 Binomial Distributions 2 Make a Plan The direct way to solve the problem is to calculate P(3) + P(4). Example 1: Problem-Solving Application You make 4 trips to a drawbridge. There is a 1 in 5 chance that the drawbridge will be raised when you arrive. What is the probability that the bridge will be down for at least 3 of your trips?

6. Holt McDougal Algebra 2 Binomial Distributions Solve 3 P(3) + P(4) = 4 C 3 The probability that the bridge will be down for at least 3 of your trips is 0.8192. Example 1: Problem-Solving Application You make 4 trips to a drawbridge. There is a 1 in 5 chance that the drawbridge will be raised when you arrive. What is the probability that the bridge will be down for at least 3 of your trips? + 4 C 4 (0.80) 3 (0.20) 1 (0.80) 4 (0.20) 0

7. Holt McDougal Algebra 2 Binomial Distributions Look Back 4 The answer is reasonable, as the expected number of trips the drawbridge will be down is of 4, = 3.2, which is greater than 3. So the probability that the drawbridge will be down for at least 3 of your trips should be greater than Example 1: Problem-Solving Application You make 4 trips to a drawbridge. There is a 1 in 5 chance that the drawbridge will be raised when you arrive. What is the probability that the bridge will be down for at least 3 of your trips?

8. Holt McDougal Algebra 2 Binomial Distributions Wendy takes a multiple-choice quiz that has 20 questions. There are 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing? Example 2: Problem-Solving Application 1 Understand the Problem The answer will be the probability she will get at least 2 answers correct by guessing. The probability of guessing a correct answer is. List the important information: Twenty questions with four choices

9. Holt McDougal Algebra 2 Binomial Distributions The direct way to solve the problem is to calculate P(2) + P(3) + P(4) + … + P(20). An easier way is to use the complement. "Getting 0 or 1 correct" is the complement of "getting at least 2 correct." Wendy takes a multiple-choice quiz that has 20 questions. There are 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing? Example 2: Problem-Solving Application 2 Make a Plan

10. Holt McDougal Algebra 2 Binomial Distributions = 20 C 0 P(0) + P(1) Step 1 Find P(0 or 1 correct). Step 2 Use the complement to find the probability. Wendy takes a multiple-choice quiz that has 20 questions. There are 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing? Example 2: Problem-Solving Application Solve 3 The probability that Wendy will get at least 2 answers correct is about 0.98. + 20 C 1 (0.25) 0 (0.75) 20 (0.25) 1 (0.75) 19

11. Holt McDougal Algebra 2 Binomial Distributions The answer is reasonable since it is less than but close to 1. Look Back 4 Wendy takes a multiple-choice quiz that has 20 questions. There are 4 answer choices for each question. What is the probability that she will get at least 2 answers correct by guessing? Example 2: Problem-Solving Application

12. Holt McDougal Algebra 2 Binomial Distributions A machine has a 98% probability of producing a part within acceptable tolerance levels. The machine makes 25 parts an hour. What is the probability that there are 23 or fewer acceptable parts? Example 3: Problem-Solving Application 1 Understand the Problem The answer will be the probability of getting 1–23 acceptable parts. List the important information: 98% probability of an acceptable part 25 parts per hour with 1–23 acceptable parts

13. Holt McDougal Algebra 2 Binomial Distributions The direct way to solve the problem is to calculate P(1) + P(2) + P(3) + … + P(23). An easier way is to use the complement. "Getting 23 or fewer" is the complement of "getting greater than 23.“ Find this probability, and then subtract the result from 1. A machine has a 98% probability of producing a part within acceptable tolerance levels. The machine makes 25 parts an hour. What is the probability that there are 23 or fewer acceptable parts? Example 3: Problem-Solving Application 2 Make a Plan

14. Holt McDougal Algebra 2 Binomial Distributions = 25 C 24 P(24) + P(25) Step 1 Find P(24 or 25 acceptable parts). A machine has a 98% probability of producing a part within acceptable tolerance levels. The machine makes 25 parts an hour. What is the probability that there are 23 or fewer acceptable parts? Example 3: Problem-Solving Application Solve 3 Step 2 Use the complement to find the probability. The probability that there are 23 or fewer acceptable parts is about 0.09. + 25 C 25 (0.98) 24 (0.02) 1 (0.98) 25 (0.02) 0

15. Holt McDougal Algebra 2 Binomial Distributions Since there is a 98% chance that a part will be produced within acceptable tolerance levels, the probability of 0.09 that 23 or fewer acceptable parts are produced is reasonable. A machine has a 98% probability of producing a part within acceptable tolerance levels. The machine makes 25 parts an hour. What is the probability that there are 23 or fewer acceptable parts? Example 3: Problem-Solving Application Look Back 4

16. Holt McDougal Algebra 2 Binomial Distributions Lesson 3.3 Practice C