A committee contains 4 men and 3 women Two members are selec

A committee contains 4 men and 3 women. Two members are selected at random to form a subcomittee. What is the probability that both are women?

A box contains 2 red balls and 3 white balls. Two balls are selected at random, without replacement. Find the probability that at least one of them is white.

Solution

a)

There are 7C2 = 21 ways to choose 2 people.

There are 3C2 = 3 ways to choose two women.

hence,

P(both women) = 3/21 = 1/7 = 0.1429 [answer]

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b)

P(at least one white) = 1 - P(no white)

There is only 1 way that we can choose no white, that is, both are red.

There are 5C2 = 10 ways to choose 2 balls.

Thus,

P(no white) = 1/10 = 0.1

Therefore,

P(at least one white) = 1 - 0.1 = 0.9 [answer]