QuantMech

^^dillbilly123, It would help you also to figure out what was wrong with your approach? Looking at what you did, the essence of your difficulty seems to be that you need to figure out exactly how to apply the counting arguments in probability.

You clearly have the basic idea that the probability is the number of ways that a particular outcome could be observed, divided by the total number of possible outcomes. The key to getting the probability questions right, though, is to understand what "particular outcome" and "total number of possible outcomes" should be involved in the calculation, and how.

You are trying to determine the probability that 2 men and 1 woman will be in the offices, given 3 men and 2 women to be assigned to offices or cubicles. So, you start by saying that the probability that it will be 2 men is 2/3, because there are 3 men. To see why this is not right, suppose that the question asked for the probability that 3 men would be in the offices, given 3 men and 2 women to be assigned to offices or cubicles. Do you see that the number of men should not be in the denominator?

The probability to assign a woman is not 1/2, in this case (unless 1 man has already been assigned to the office). If you had two women (Doris and Chloris), and you knew that one had been assigned an office randomly, the probability that it was Doris is 1/2. But that's not what this question is asking. So the number of women shouldn't be in the denominator, either.

Another way to look at it--for the purpose of understanding the probability calculation now, so that you can handle it on the SAT later, not for the purpose of going through this train of thought on the actual test--is to think about the case where there are 3 men and 200 women, and 3 people are going to be assigned to offices. The odds of 2 men being assigned to the offices would (pretty obviously) not be 2/3 in this case.