The Computer Systems Department has eight faculty six of who

The Computer Systems Department has eight faculty, six of whom are tenured. Dr. Vonder, the chair, wants to establish a committee of three department faculty members to review the curriculum. If she selects the committee at random:

a.   What is the probability all members of the committee are tenured?

b.   What is the probability that at least one member is not tenured? (Hint: For this question, use the complement rule).

Solution

Answer :-

a)The total number of ways to choose 3 members out of 8 is

C(8, 3) = 8!/(3! 5!) = (8*7*6*5*4*3*2*1) / ((3*2*1) * (5*4*3*2*1)) = 56.

The total number of ways to choose 3 tenured people from 6 is

C(6,3) = 6!/(3! 3!) = (6*5*4*3*2*1) / ((3*2*1) * (3*2*1)) = 20. So the probability is

P(all members of the committee are tenured) = 20/56 = 5/14 = 0.3571

b) Probability (at least one member is not tenured) = 1 - Probability(All three are tenured)

= 1- 5/14 = 9/14

=0.6429