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Probability

Assume 11 males audition, one of them being Winston, 4 females audition, one of them being Margaret, and 5 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.
 
What is the probability (if the roles are filled at random) of both Winston and Margaret getting a part?
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1 Answer

We can ignore the children, since they don't affect the probability of both Winston and Margaret getting parts. Winston's probability is 3/11 and Margaret's is 1/4. These events are independent, so the probability of both of them happening is  3/11 x 1/4 = 3/44.
 
However, if the roles are being filled at random, why have auditions? Whey not just draw names out of a hat and save everyone the trouble?