An Economic Department at a state university with five faculty members-Anderson, Box, Cox, Carter, and Davis-must select two of its members to serve on a program review committee. Because the work will be time-consuming, no one is anxious to serve, so it is decided that the representative will be selected by putting five slips of paper in a box, mixing them, and selecting two.
a. What is the probability that both Anderson and Box will be selected? (Hint: List the equally likely outcomes.)
b. What is the probability that at least one of the two members whose name begins with C is selected?
c. If the five faculty members have taught for 3, 6, 7, 10, and 14 years, respectively, at the university, what is the probability that the two chosen representatives have at least 15 years' teaching experience at the university?

Question

Quizplus · Accepted Answer

The Answer is Outcomes:
(A, B), (A,

C _ { 1 }

), (A,

\mathrm { C } _ { 2 }

), (A,D), (B,A), (B,

C _ { 1 }

), (B,

\mathrm { C } _ { 2 }

), (B,D), (

C _ { 1 }

,A), (

C _ { 1 }

,B), (

\mathrm { C } _ { 1 } , \mathrm { C } _ { 2 }

), (

C _ { 1 }

,D), (

\mathrm { C } _ { 2 }

,A), (

\mathrm { C } _ { 2 }

,B), (

\mathrm { C } _ { 2 } , \mathrm { C } _ { 1 }

), (

\mathrm { C } _ { 2 }

,D), (D,A), (D,B), (D,

C _ { 1 }

), (D,

\mathrm { C } _ { 2 }

)
a. P[(A,B) or (B,A)] = 2 / 20 = .10
b. P(at least one C) = 14 / 20 = .70
c. P(at least 15 years) = 1 - P(at most 14 years)
= 1 - P[(3,6) or (6,3) or (3,7) or (7,3) or (3,10) or (10,3) or (6,7) or (7,6)]
= 1 - 8 / 20 = .60

An Economic Department at a State University with Five Faculty