If P(R-intersect-S|S) = 20/29, P(R\S)=(2/3)P(W), find number

Phillip

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May 5, 2009
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I have no idea how to do this problem, I feel as if there isn't enough information given to solve it. If anyone could at least point me in the right direction it'd be extremely helpful.

A small gym owns 162 towels: red (R), blue striped (S), red with blue stripes (R ? S), and white (W). If:
• The probability a towel is red given that it has blue stripes is 20/29 : Pr(R ? S |S ) = 20/29
• You are 2/3 as likely to get a white towel as you are to get a red towel with no stripes: Pr(R \ S) = (2/3)Pr(W)

(a) How many white towels are there?
(b) What is the probability of getting a striped towel?

Thanks to anyone who can at least get me started.
 
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