Problem:
The Belgian 20-Frank coin (B20), the Italian 500-Lire coin (L500), and the Hong Kong 5-Dollar (HK5) are approximately the same size. Coin purse one (C1) contains six of each of these coins. Coin purse two (C2) contains nine B20s, six I500s, and three HK5s. A fair four-sided die is rolled. If the outcome is {1}, a coin is selected randomly from C1. If the outcomes belong to {2, 3, 4}, a coin is selected randomly from C2.
a) Find P(HK5).
b) Find P(C2|HK5).
I've drawn a tree diagram.
Now for a), is this correct?