(a) Write out a formula for the probability distribution of the 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 three decimal places.) P(1) =   P(2) =   P(3) =   (c) Compute the probability that n ≥ 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.)

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Use the geometric probability distribution to solve the following problem.

On the leeward side of the island of Oahu, in a small village, about 71% 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) = 

(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) =  
P(2) =  
P(3) =  

(c) Compute the probability that n ≥ 4. HintP(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.)

 
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