Use thegeometric probability distributionto solve the following problem.

On the leeward side of the island of Oahu, in a small village, about70%of the residents are of Hawaiian ancestry. Letn= 1, 2, 3, ... represent the number of people you must meet until you encounter thefirstperson of Hawaiian ancestry in the village.

(a)Write out a formula for the probability distribution of the random variablen. (Enter a mathematical expression.)

P(n) =

(b)Compute the probabilities thatn= 1,n= 2, andn= 3. (For each answer, enter a number. Round your answers to three decimal places.)

P(1) =

P(2) =

P(3) =

(c)Compute the probability thatn?4.Hint:P(n?4) = 1?P(n= 1)?P(n= 2)?P(n= 3). (Enter a number. Round your answer to three decimal places.)

(d)What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry?Hint: Use?for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.)

Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 70% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, represent the number of people you must meet until you encounter the rst person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = 9(1-p)"n-1 x (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1)= .700 y P(2) = .182 x P(3) = .047 x (c) Compute the probability that n 2 4. Hint: P(n 2 4) = 1 P(n = 1) P(n = 2) - P(n = 3). (Enter a number. Round your answer to three decimal places.) .058 X (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use it for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) 1 ./ residents