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Section 8.2 Geometric Distributions AP Statistics The Geometric Setting 1. 2. 3. 4. Each observation falls into one of just two categories, which for convenience we call “success” or “failure” You keep trying until get a success The observations are all independent. The probability of success, call it p, is the same for each observation. AP Statistics, Section 8.2.2 2 Calculating Probabilities The probability of rolling a 6= The probability of rolling the first 6 on the first roll: The probability of rolling the first 6 after the first roll: AP Statistics, Section 8.2.2 3 Calculating Probabilities The probability of rolling a 6=1/6 The probability of rolling the first 6 on the second roll: The probability of rolling the first 6 on the second roll or before: AP Statistics, Section 8.2.2 4 Calculating Probabilities The probability of rolling a 6=1/6 The probability of rolling the first 6 after the second roll: AP Statistics, Section 8.2.2 5 You can use these formulas n 1 P( X n) pq , geometpdf(p,n) P( X n) 1 p , 1-geometcdf(p,n) n P( X n) 1 1 p , geometcdf(p,n) n AP Statistics, Section 8.2.2 6 Formulas for Geometric Distribution 1 X p 1 p 1 p 2 , X 2 p p 2 X AP Statistics, Section 8.2.2 7 In New York City at rush hour, the chance that a taxicab passes someone and is available is 15%. a) How many cabs can you expect to pass you for you to find one that is free b) what is the probability that more than 10 cabs pass you before you find one that is free. Examples You are a barista at Starbucks. The probability that a customer orders a "Holiday Drink" is 0.7. Assume that drink orders are independent. Find the following probabilities: What is the probability that 5 of the next 10 customers order a holiday drink? What is the probability that it takes fewer than 3 customers before someone orders the first holiday drink? What is the probability that at least 6 of the next 10 customers order a holiday drink? How many customers out of the next 10 customers would you expect to order a holiday drink? How many customers do you expect to order before you get your first holiday drink order? What is the probability that 5 customers order before someone orders a holiday drink? AP Statistics, Section 8.2.2 9