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Unit: Probability 12-6: Binomial Distributions

Unit: Probability 12-6: Binomial Distributions. Essential Question: Why, for a binomial probability, p + q must equal 1. 12-6: Binomial Distribution. Write your name on a piece of paper. Make two columns. Number each column 1 – 6.

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Unit: Probability 12-6: Binomial Distributions

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  1. Unit: Probability12-6: Binomial Distributions Essential Question: Why, for a binomial probability, p + q must equal 1

  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

  4. 12-6: Binomial Distribution • A binomial experiment has three important features: • The situation involves repeated trials • Each trial has two possible outcomes • Success or failure • 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: • nCxpxqn-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 • 50%, or 0.5 • 4, 5 or 6 correct • 6C4 • .54 • .52 = 0.234375 • 6C5 • .55 • .51 = 0.09375 • 6C6 • .56 • .50 = 0.015625 • 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 • 75%, or 0.75 • 4, 5 or 6 correct • 6C4 • .254 • .752 ≈ 0.03296 • 6C5 • .255 • .751≈ 0.00439 • 6C6 • .256 • .750≈ 0.00024 • 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 • 4C4 • .904 • .100 = 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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