On the leeward side of the island of Oahu, in a small village, about 81% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, ... represent the number of people you must meet until you...

On the leeward side of the island of Oahu, in a small village, about 81% of the residents are of Hawaiian ancestry. Letn = 1, 2, 3, ... represent the number of people you must meet until you encounter thefirst person 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.)