SOLUTION: The Internal Revenue Service is studying the category of charitable contributions. A sample of 26 returns is selected from young couples between the ages of 20 and 35 who had an ad

Question 1043562: The Internal Revenue Service is studying the category of charitable contributions. A sample of 26 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 26 returns, 6 had charitable contributions of more than $1,000. Suppose 5 of these returns are selected for a comprehensive audit.
1.What is the probability exactly one of the five audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)
2.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 Boreal(15235) (Show Source): You can put this solution on YOUR website!
Probability of none having a deduction more than $1000 is (20/26)(19/25)(18/24)(17/23)(16/22)=
1860480/7893600=0.2357. Therefore, the probability of at least one is 1-0.2357=0.7643.
The probability of exactly one has the same denominator.
The numerator has 20,19,18,17,and 6, and they can be ordered 5 ways, so multiply those five numbers by 5.
2907000/7893600=0.3683
This makes intuitive sense. About a quarter of the returns have >$1000, so the expected value is a little larger than 1. The value for 2 is 0.26, not as large as that for 1, and for 3 is 0.0578.
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