The Internal Revenue Service is studying the category of cha

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.

Solution

There are 18 returns.

4 of which had contribution > $1000

Hence, p of getting >$1000 person is 4/18

Suppose 3return are selected, Prob of finding >$100,000 return people?

We use the binominal theorm :

18C3 ( 4/18)^3 * (14/18)^15

=.2065

So, Probability of getting 3 of these retuen in comprehensive audit is 20.65% or .2065