Jack likes to go fishing. While waiting for the fishes to bite, he formulates the following model for the process: fishes bite according to a Poisson process with intensity 4 bites per hour. Biting fishes are caught independently, and on average only one in two times.

a) What is the probability that six fishes bite during the first two hours?

b) What is the probability that he fails to catch any fishes during the first two hours?

c) What is the probability that, during the first two hours, six fishes bite and two of these are caught?