SOLUTION: A company is to hire two new employees. They have prepared a final list of eight candidates, all
of whom are equally qualified. Of these eight candidates, five are women. Suppose
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of whom are equally qualified. Of these eight candidates, five are women. Suppose
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Question 1168078: A company is to hire two new employees. They have prepared a final list of eight candidates, all
of whom are equally qualified. Of these eight candidates, five are women. Suppose the
company decides to select two persons randomly from these eight candidates.
a. What is the probability that:
i. Both candidate selected are women?
ii. At least one candidate selected is a woman?
iii. Second candidate is a woman.
iv. First candidate is a woman given that the second candidate is a woman.
b. Let X denote the number of women in this sample.
i. Write the probability distribution of X.
ii. Find the standard deviation of X. Answer by ikleyn(52803) (Show Source):
I will answer three questions of the part (a), ONLY.
(i) What is the probability that bothselected are women?
P = P(1st candidate is woman)*P(2nd candidate is woman) = = = . ANSWER
(ii) What is the probability that at least one candidate selected is a woman?
It is the COMPLEMENT to the probability that both candidates are men
P = 1 - = 1 - = = = . ANSWER
(iii) What is the probability that second candidate is a woman?
P = P(1st is M)*P(2nd is W) + P(1st is W)*P(2nd is W) = = + = = . ANSWER
