1. Essential Question: How do you calculate the probability of a binomial experiment?

2.  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.  Answers (T/F)Answers (A/B/C/D) 1FD 2TB 3FC 4FC 5TB 6FA

4.  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 r successes in n trials is the following product:  n C r p r q n-r

5.  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.  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.  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.  As the number of experiments grows, the shape of a binomial distribution approaches a (symmetric) normal curve  The expected value of a binomial distribution is np, where n = the number of trials and p = the probability of success  The standard deviation of the binomial distribution is npq, where q is the probability of failure

9.  Assignment  Page 889  Problems 1 – 16  Tip for #s 14 – 16 ▪ 14 asks for the expected value of the probability distribution ▪ 15 uses that number for µ