SOLUTION: A committee is composed of six democrats and five republicans. three of the democrats are men and three of the republicans are men. if a man is chosen for chairman, what is the pro

Question 883998: A committee is composed of six democrats and five republicans. three of the democrats are men and three of the republicans are men. if a man is chosen for chairman, what is the probability that he is a republican?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability that the chairman will be a man and a republican at the same time is 3/11 because there are only 3 male republicans out of the 11 candidates.

the probability that the chairman will be a male is equal to 6 out of 11 because there are 6 male candidates out of 11 (3 democrats and 3 republicans).

given that a man is chosen as chairman, the probability that he will be a republican is given by the formula:

p(republican given male) = p(male and republican) / p(male).

this formula becomes p(republican given male) = (3/11) / (6/11) which is equal to (3/11) * (11/6) which is equal to (3/6) which is equal to (1/2).

looked at another way, if the chairman is a male, the probability that he will be a republican is equal to 3/6 because there are 6 male candidates and 3 of them are republican.

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