Question

An academic department with five faculty members—Anderson, Box, Cox, Cramer, and Fisher—must select two of its members to serve on a personnel review committee. Because the work will be time–consuming, no one is anxious to serve, so it is decided that the representatives 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 proba

Answer 1

Answer:

(a) 0.10

(b) 0.70

(c) 0.30

Step-by-step explanation:

Items b and c are missing from the question:

(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 a total of at least 18 years teaching experience there?

The number of ways to select two representatives out of 5 people is given by the combination of picking two out of 5:

$n=\frac{5!}{(5-2)!2!}\\n=10\ ways$

(a) Since there is only one way for both Anderson and Box to be selected, the probability is:

$P = \frac{1}{10}=0.10$

(b) There are four ways for Cox to be selected, four ways for Cramer to be selected, and one where both are selected. The probability is:

$P =\frac{4+4-1}{10}=0.7$

(c) The only possible ways for the total of number of years to exceed 18 is by selecting: (14;6 14;7 14;10). Therefore the probability is:

$P = \frac{3}{10}=0.30$