Question

On the leeward side of the island of Oahu, in the small village of Nanakuli, about 80% 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 of Nanakuli.

(a) Write out a formula for the probability distribution of the random variable n.
(b) Computer the probability that n=1, n=2, n=3.
(c) Compute the probability that n is greater than or equal to 4.
(d) In Waikiki it is estimated that about 4% of the residents are of Hawaiian ancestry. Repeat parts (a) (b) and (c) for Waikiki.

Answer 1

a) p(1-p)^n-1