Probability of a fisherman
Every day a fisherman can choose to fish at sea, by a river, or at a lake. The probability that he fishes at sea, by the river, and at the lake are 1/2, 1/4 and 1/4 resp. If he goes out to sea to fish, his chances of catching some fish is 80%, while his chances of catching some fish at the river and the lake are 40% and 60% respectively.
a. Find the probability that the fisherman catches fish on a randomly chosen day.
b. If one day the fisherman does not catch any fish, determine the place he most probably has chosen to fish.