2 >|x-y| >0.44 = 1.56/2 = 0.78 = P(A) ?
For (B) = use law of total probability = (P(over)P(under))+(P(under)P(over))
=(1.56/2)x(0.44/2)+(0.44/2)+(1.56/2) = .34
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) =