Great work, goyalsau:
These "multiple categories" problems are great exercises in staying organized with information. Here, if you break down what you know:
10 democrats, 10 republicans
11 women, 9 men
7 women democrats --> the other 4 women are republicans
4 women republicans --> the other 6 republicans are men
6 male republicans / 20 total people = 6/20 or 3/10 chance of picking a male republican.
One helpful strategy in problem solving is to "follow the data" - use what you know to solve for the next unknown, and you'll follow a path toward filling in all the blanks.
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One other note: someone posted on this board today that they were having trouble with probability in general. I'd argue that at least 1/3 of "probability" questions aren't probability questions at all - they're, like this one, problems in which your final answer is EXPRESSED as a probability, but really they're arithmetic/algebra problems that simply require as a final step your knowledge that:
Probability of A = # of A outcomes / # of total outcomes
As long as you know the number of total outcomes and the number of those that get you what you want, you just have to express your answer as a fraction and the whole thing is solved.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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