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.

Question

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.

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