Find the indicated probabilities using the geometric distribution, the Poisson d

Question

Find the indicated probabilities using the geometric distribution, the Poisson distribution, of the binomial distribution. Then determine whether the events are unusual. Problem: One out of every 100 tax returns that a tax auditor examines requires an audit. Find the probability that (A) the first return requiring an audit is the 25th return the tax auditor examines (B) the first return requiring an audit is the first or second return the tax auditor examines, and (C) none of the first five returns the tax auditor examines requires an audit.

Explanation / Answer

Find the probability that (

A) the first return requiring an audit is the 25th return the tax auditor examines

Prob = 1/100 * 99/100 ^25-1 = 0.00786

(B) the first return requiring an audit is the first or second return the tax auditor examines,

Prob = 1/100^2 = 0.0001

(C) none of the first five returns the tax auditor examines requires an audit.

P(x=0) = 5C0 * (1/100)^0 * (99/100)^5-0

P(x=0)= 0.95099

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