Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 22 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 22 returns 7 had charitable contributions of more than $1,000. Suppose 6 of these returns are selected for a comprehensive audit.What is the probability exactly one of the six audited had a charitable deduction of more than $1,000? What is the probability at least one of the audited returns had a charitable contribution of more than $1,000?
This is not a binomial distribution, but rather, a hypergeometric distribution. (since the samples are taken all at once and so, each sample is dependent, and is actually similar to an experiment of without replacement)
