.Alice and Bob each choose a number is the interval [0, 2]. We assume a uniform probability law, so that 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 less than 1/3. B: At least one of the numbers is smaller than 1/3. C: The two numbers are equal. D: Alice's number is greater than 1/3. Find the probabilities P(B), P(C) and P(A D).