Stark’s Pond contains 10 trout and 5 bluegill fish.  Kyle catches a random number of fish (call the number \(X\)), where \(X \sim \text{Unif}(\{1,\ldots,4\})\).  Once caught, that fish is removed from the pond and cannot be caught again.  Each new fish comes uniformly from the remaining fish.

(a) What is the chance that Kyle catches all trout?

(b) Suppose all the fish that Kyle caught were trout.  Given this information, what is the probability that he caught exactly 5 fish?

[Author Mark Huber. Licensed under Creative Commons.]