2 Assume that each year the IRS randomly audits 4 of the tax

2. Assume that each year the IRS randomly audits 4% of the tax returns. If a married couple has filed separate returns, what is the probability that: A. both the husband and the wife will be audited? B. either the husband or the wife will be audited? C. neither will be audited?

Solution

Sol)

chance of being audit = 0.04
chance of not = 1 - 0.04 = 0.96

A. Probability that both the husband and the wife will be audited

P(A and B) =P(A)*P(B)

P(A and B) = 0.04 *0.04 = 0.0016

B) Probability that  either the husband or the wife will be audited

P(either A or B) = 0.04*096 +0.96*0.04 = 0.0768

C) Probability that neither the husband nor the wife will be audited= 0.96*0.96 =0.9216