SOLUTION: The Internal Revenue Service is studying the category of charitable contributions. A sample of 18 returns is selected from young couples between the ages of 20 and 35 who had an ad

Question 1066123: The Internal Revenue Service is studying the category of charitable contributions. A sample of 18 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 18 returns, 4 had charitable contributions of more than $1,000. Suppose 3 of these returns are selected for a comprehensive audit.
What is the probability exactly one of the three audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)

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.)

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The Internal Revenue Service is studying the category of charitable contributions. A sample of 18 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 18 returns, 4 had charitable contributions of more than $1,000.
P(an individual has contributions >= 1000) = 4/18 = 2/9
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Suppose 3 of these returns are selected for a comprehensive audit.
What is the probability exactly one of the three audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)
Binomial Problem with n = 3 and p = 2/9
P(x = 1) = 3C1*(2/9)*(7/9)^2 = binompdf(3,2/9,1) = 0.4033
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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.)
P(1<= x <=3) = 1-P(x=0) = 1-(7/9)^3 = 0.5295
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Cheers,
Stan H.
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