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

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Presentation transcript:

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

 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

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

 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

 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 C = C = C = = , or 34.4%

 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 , 5 or 6 correct 75%, or C ≈ C ≈ C ≈ = , or 3.8%

 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 %, or C = , or 65.61%

 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

 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