GRE Probability and Statistics 2?

Question

John invites 12 friends to a dinner party, half of which are men. Exactly one man and one woman are bringing desserts. If one person from this group is selected at random, what is the probability that it is a woman, OR a man who is not bringing a dessert? The above question is a GRE practice question and the answer is 11/12.

Answer 1

Of the 12 guests, we want to identify how many fall under one of the two criteria:

1. the guest is a woman, or
2. the guest is a man who is not bringing dessert.

Based on the information given, we know that 6 of the 12 guests (half) are women, and of the 6 male guests, only one is bringing dessert, so that leaves 5 male guests who are not bringing dessert.

So we have 6 guests that are women, and 5 guests that are men who are not bringing desserts. So the probability of selecting a guest at random who is either a woman (6) or a man not bringing a dessert (5) is 11/12.

Answer 2

If half of 12 are men, this implies there are 6 men, and also that there are 6 women.

If exactly 1 man is bringing dessert, and exactly 1 woman is bringing dessert, the probability of:

P(W) + P(Man, no dessert) is 6/12 + 5/12 = 11/12