Alice and Bob each choose at random a number between zero and two. 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 0.44.

B: At least one of the numbers is greater than 0.44.

C: The two numbers are equal.

D: Alice's number is greater than 0.44.

Find the following probabilities.

P(A) =

P(B) =

P(A∩B) =

P(C) =

P(D) =

P(A∩D) =