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Essential Question: Why, for a binomial probability, p + q must equal 1 Unit: Probability 12-6: Binomial Distributions.

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Presentation on theme: "Essential Question: Why, for a binomial probability, p + q must equal 1 Unit: Probability 12-6: Binomial Distributions."— Presentation transcript:

1 Essential Question: Why, for a binomial probability, p + q must equal 1 Unit: Probability 12-6: Binomial Distributions

2 12-6: Binomial Distribution Write your name on a piece of paper Make two columns Number each column 1 – 6 DO NOT DISCUSS YOUR ANSWERS WITH YOUR NEIGHBORS – you will mess up this experiment In the first column, for questions 1 – 6, answer “T” or “F” In the second column, for questions 1 – 6, answer “A”, “B”, “C”, or “D” Exchange your paper with a partner for them to grade

3 12-6: Binomial Distribution Answers (T/F)Answers (A/B/C/D) 1FD 2TB 3FC 4FC 5TB 6FA

4 12-6: Binomial Distribution A binomial experiment has three important features: 1) The situation involves repeated trials 2) Each trial has two possible outcomes Success or failure 3) The probability of success is constant throughout the trials The trials are independent Suppose you have repeated independent trials, each with a probability of success p and a probability of failure q (with p + q = 1). Then the probability of x successes in n trials is the following product: n C x p x q n-x

5 12-6: Binomial Distribution Suppose you guess the answer to six questions on a true or false test. What is the probability of you passing the test? What is the probability of success? What is the probability of failure? What are the situations where you pass? Find the probability of 4/5/6 correct answers out of 6 questions So the probability of you passing is 50%, or 0.5 4, 5 or 6 correct 50%, or 0.5 6 C 6.5 6.5 0 = 0.015625 6 C 5.5 5.5 1 = 0.09375 6 C 4.5 4.5 2 = 0.234375 0.234375 + 0.09375 + 0.015625 = 0.34375, or 34.4%

6 12-6: Binomial Distribution What if the test was multiple choice test with four possible answers. What is the probability of you passing the test? What is the probability of success? What is the probability of failure? What are the situations where you pass? Find the probability of 4/5/6 correct answers out of 6 questions So the probability of you passing is 25%, or 0.25 4, 5 or 6 correct 75%, or 0.75 6 C 6.25 6.75 0 ≈ 0.00024 6 C 5.25 5.75 1 ≈ 0.00439 6 C 4.25 4.75 2 ≈ 0.03296 0.03296 + 0.00439 + 0.00024 = 0.03759, or 3.8%

7 12-6: Binomial Distribution A calculator contains 4 batteries. With normal use, each battery has a 90% chance of lasting one year. What is the probability that all four batteries will last a year? What is the probability of success? What is the probability of failure? Find the probability of 4 out of 4 lasting batteries 90%, or 0.90 10%, or 0.10 4 C 4.90 4.10 0 = 0.6561, or 65.61%

8 12-6: Binomial Distribution Assignment Page 688 – 689 Problems 1 – 14, all Ignore the directions: For #1 – 3, find the theoretical probability instead of the experimental For #4 – 7, don’t worry about the tree diagram For #12 – 14, find all breakdowns for n = 6 (including when x = 0) Plan for the week Monday, 12-6 Tuesday, 12-3 Wednesday, Test Preview Thursday, Probability Test

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