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 isproportionalto 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 probabilitiesP(B),P(C) andP(A∩D).