5. An Economic Department at a state university with five faculty members - Ande

Question

5. 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. 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?

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?

Explanation / Answer

a) P(both Anderson and Box Will be selected) = 1/Number of ways in which 2 people can be selected

= 1 / 5C2

= 1 / 10

= 0.1

b) P(at least one of the two members whose name begins with C?) = 1 - P(both names do not begin with C)

= 1 - 3C2/5C2

= 1 - 3/10

= 0.7

c) The sum of ages will be above 15 in the following cases

(14,10), (14,7), (14,6), (14,3), (10,7), (10,6) = 6 cases

Number of selections possible = 5C2 = 10

P(two chosen representatives have at least 15 years’ teaching experience at the university) = 6/10

= 0.6

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.