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 first 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) = (0.7)~(n-1)*(0.3) 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) = 0.21 P(2) = 0.147 XXX P(3) = 0.1029 (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.) 0.640 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 u for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) 5 x residents