Alice and Bob each choose at random a number in the interval [0, 2]. We assume a uniform probability law under which the probability of an event is proportional to its area. Consider the following events:

a. The magnitude of the difference of the two numbers is greater than 1/3.b. At least one of the numbers is greater than 1/3.c. The two numbers are equal. d. Alice's number is greater than 1/3.Find the probabilities P(A), P(B), P(A∩B),