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 representative will be selected by putting the names on identical pieces of paper and then randomly selecting two.

(a) What is the probability that both Anderson and Box will be selected?

answer 0.1 or 1/10


(b) What is the probability that at least one of the two members whose name begins with C is selected?

answer 0.7 or 7/10


(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 14 years teaching experience there?

I need answer for C? Don't understand.

There are five faculty members in a certain academic department. These individuals have 3, 6, 7, 10, and 15 years of teaching

0.52

To find the probability that the two chosen representatives have a total of at least 14 years of teaching experience, we need to consider the different combinations of faculty members and their years of experience.

Let's list all possible combinations of two faculty members and their total years of experience:

1. Anderson (3 years) + Box (6 years) = 9 years
2. Anderson (3 years) + Cox (7 years) = 10 years
3. Anderson (3 years) + Cramer (10 years) = 13 years
4. Anderson (3 years) + Fisher (14 years) = 17 years
5. Box (6 years) + Cox (7 years) = 13 years
6. Box (6 years) + Cramer (10 years) = 16 years
7. Box (6 years) + Fisher (14 years) = 20 years
8. Cox (7 years) + Cramer (10 years) = 17 years
9. Cox (7 years) + Fisher (14 years) = 21 years
10. Cramer (10 years) + Fisher (14 years) = 24 years

Out of these combinations, there are 4 combinations where the total years of experience are at least 14 (combinations 4, 6, 8, and 9).

Since there are a total of 10 possible combinations, the probability that the two chosen representatives have a total of at least 14 years of teaching experience is 4/10 or 0.4.

Thus, the answer to part (c) is 0.4 or 4/10.

Solution of this question

3, 14

6, 10 or 6, 14
7, 10 or 7, 14
10, 14

It looks like there are 6 possibilities that meet this criteria because they all add up to at least 14 which means 14 or more years

If we choose two out of 5

Use a combination of 2 chosen from 5 which is 5!/(3! 2!) = 10 choices
! means multiply down to 1. So, 5! means 5 x 4 x 3 x 2 x1.

You had 6 possibilities out of 10 choices or .6