IRS data show that 16 of personal tax returns reporting an a

IRS data show that 16% of personal tax returns reporting an adjusted gross income more than $1,000,000 will be subject to a computer audit. This year a CPA completed 18 returns with adjusted gross incomes more than $1,000,000. The CPA wants to know the likelihoods that the returns will be audited. a. What probability distribution applies to this situation? b. What is the probability exactly one of these returns is audited? c. What is the probability at least one of these returns is audited?

Solution

A)

This is a BINOMIAL PROBABILITY DISTIRBUTION.

This is so because there are only 2 outcomes, success and failure. Also, the trials are independent, and the probability of success is constant. The number of trials is also constant.

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b)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    18      
p = the probability of a success =    0.16      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.148641593 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    18      
p = the probability of a success =    0.16      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.043353798

Thus,

P(at least 1) = 1- P(0) = 1 - 0.043353798 = 0.956646202 [ANSWER]