Refer to Exercise 5. Two candidates are randomly selected.
a. List the equally likely outcomes.
b. What is the probability that both are qualified?
c. What is the probability that exactly one is qualified?
(a) The equally likely outcomes are the sequences of two distinct candidates. These are {12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, 43}.
(b) Of the 12 equally likely outcomes, there are 2 (12 and 21) for which both candidates are qualified. The probability is therefore 2?12 or 1?6.
(c) Of the 12 equally likely outcomes, there are 8 (13, 14, 23, 24, 31, 32, 41, and 42) for which exactly one candidate is qualified. The probability is therefore 8?12 or 2?3.
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