Probabillity Question

Question

Two people are selected at random from eleven men and ten women. Find the probability that the first is a woman and the second is a man.

Answer 1

so 11/21 are men and 10/21 are women.

The probability of getting a woman on the first selection is simply 10/21. What we need to do know is to figure out the probability of getting a man on the second selection, given that we selected a woman on the first. But first, one caveat—the question doesn't say whether the individuals are selected with or without replacement. This affects the answer, so I'll respond to both possibilities. In either case, we simply multiply the probability of the first selection by the probability of the second.

So with replacement, the probability is 10/21 x 11/21. Without replacement, it's 10/21 x 11/20.

Hope that helps!