On the leeward side of the island of Oahu, in a small village, about72%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.)

(a) 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 thatn4.Hint:P(n4) = 1P(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: Usefor the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents