1. The problem statement, all variables and given/known data Another challenging question about probability.............. Originial question: A factory produces two types of shirt: shirt A and shirt B. Each type of shirt has 3 sizes: small (S), medium (M) and large (L). The number of shirt A produced and the number of shirt B produced are in a ratio 2:3. For each type of shirt, the number of shirts in S, M, L sizes are in the ratio 2:5:3 (a) If a shirt is chosen at random, find the probability that it is shirt A in S size. (b) If a shirt is chosen at random and found to be size S, find the probability that it is shirt B. 2. Relevant equations 3. The attempt at a solution (a) (2/5) x (2/10) (my approach is the proportion of shirt A multiply the proportion of small size, i don't know if it's true.) (b) I think it is a conditional probablilty problem but i am not sure. I can construct the equation. It should be P(shirt B | size S) = P ( B and S ) / P(S) then i come into problem , i don't know what P(S) and P(B and S) should be. Thank you for help.