Suppose the Internal Revenue Service is studying the categor

Suppose the Internal Revenue Service is studying the category of charitable contribution. A sample of 20 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100.000 . of these 20 returns 6 had charitable contributions of more than $1,000. Suppose 4 of these returns are selected for a comprehensive audit.

a) What is the probability exactly one of the four audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places)

b) What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 4 decimal places)

Solution

a)

There are 20C4 ways to choose any four.

There are 6C1 ways to choose one that is more than 1000, and 14C3 ways to choose those 3 under 1000.

Thus,

P(1 is more than 1000) = [(6C1) (14C3)] / [20C4]

= 0.450773994 [ANSWER]

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b)

P(at least one more than 1000) = 1 - P(none is more than 1000)

There are 14C4 ways to choose any 4 that is not more than 1000.

Thus,

P(at least one more than 1000) = 1 - P(none is more than 1000)

= 1 - (14C4)/(20C4)

= 0.793395253 [ANSWER]