Suppose the Internal Revenue Service is studying the categor

Suppose 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.

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.)

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

probability that persons had a charitable deduction of more than $1,000= 6/26

now number of persons who had a charitable deduction of more than $1,000 follows binomial distriburion with n = 5 and p =6/26

b) ⁵C₁ (6/26) (20/26)^4 = 0.403994

C) probability at least one of the audited returns had a charitable contribution of more than $1,000

= P(X>=1)

=1-P(X<1)

= 1- P(X=0)

1- ⁵C₀ (6/26)^0 (20/26)^5

=1-0.269329

=0.730671