SOLUTION: A company is to hire two employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of these eight candidates, five are women. If the compan
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Question 1145316: A company is to hire two employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of these eight candidates, five are women. If the company decides to select two persons randomly from these eight candidates, what is the probability that:
i. Both candidates are women.
ii. The second candidate is a woman.
iii. The first candidate is a woman given that second one is a woman.
(i) P = = = .
The formula is self-explanatory.
(ii) P = P(first is a man; second is a women) + P(first is a woman and second is a women) = + = = = .
(iii) The given fact that the second candidate was a women, means that the first candidate-women was selected among other four women.
The conditional probability to have such a selection is .
Simply saying, the selection in this case is made entirely among 5 women.
