+-3 points My Notes Ask Your Teacher An academic department with five faculty me
ID: 3277389 • Letter: #
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+-3 points My Notes Ask Your Teacher 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? [Hint: List the equally likely outcomes. (b) What is the probability that at least one of the two members whose name begins with Cis 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 15 years teaching experience there? Need Help?Read It Talk to a Tutor It[Talk to a TutorExplanation / Answer
(a) There is only one way in which the two people selected are Anderson and Box.
Altogether there are 5C2 = 10 ways.
=> Probability that both Anderson and Box are selected = 1/10 = 0.1
(b) If Cox is one to be selected, number of second selections = 4.
If Cramer is the one to be selected, number of second selections = 4.
Thus total number of ways Cox or Cramer will be selected = 8.
However, we counted both Cox and Cramer being selected twice. So the actual count is 7.
Probability = 7 / 5C2 = 7 / 10 = 0.7
(c) The ways in which the teaching experience adds to less than 15 are
3 + 6
3 + 7
3 + 10
6 + 7
These are 4 in number and the number of ways to select two members with experience 15 or more
= 6.
Probability = 6 / 10 = 0.6
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