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

a)

There are 6C3 = 20 ways to choose 3 tenured.

There are 8C3 = 56 ways to choose any 3.

Hence,

P = 20/56 = 5/14 = 0.357142857 [ANSWER]

*******************
b)

P(at least one not teured) = 1 - P(all are tenured)

= 1 - 0.357142857

= 0.642857143 [or, 9/14] [ANSWER]