1. Use the geometric probability distribution to solve thefollowing problem.
On the leeward side of the island of Oahu, in a small village,about 80% of the residents are of Hawaiian ancestry. Let n = 1, 2,3, … represent the number of people you must meet until youencounter the first person of Hawaiian ancestry in thevillage.
(a) Write out a formula for the probability distribution ofthe random variable n. (Enter a mathematical expression.)
P(n) = _______
(b) Compute the probabilities that n = 1, n = 2, and n = 3.(For each answer, enter a number. Round your answers to threedecimal places.)
P(1) = ________
P(2) = _____
P(3) = ______
(c) Compute the probability that n ⥠4. Hint: P(n ⥠4) = 1â' P(n = 1) â' P(n = 2) â' P(n = 3). (Enter a number. Round youranswer to three decimal places.)
(d) What is the expected number of residents in the villageyou must meet before you encounter the first person of Hawaiianancestry? Hint: Use μ for the geometric distribution and round.(Enter a number. Round your answer to the nearest wholenumber.)
residents
