Probability: Calculate two events.

Question

Let A and B be two events belonging to the same sample space, such that P (A) = 1/2, P(B) = 3/5 and P (A ∩ B) = 1/4. Calculate the probabilities of upcoming events:

1. At least A or B occurs.
2. A occurs but not B
3. B occurs but not C
4. A and B occurs.
5. Neither A nor B occurs.

I'm stuck because it's set as P (A ∩ B) = 1/4. If the question didn't have it, I would calculate and reach 0.3 for P (A ∩ B). But, that's what I got.

Answer 1

P(A or B) = P(A) + P(B) - P(A and B) = 1/2 + 3/5 - 1/4 = 17/20

P(A and not B) = P(A) - P(A and B) = 1/2 - 1/4 = 1/4

P(B and not A) = P(B) - P(A and B) = 3/5 - 1/4 = 7/20 (assume, since C not given)

P(A and B) = 1/4 (given)

P(not(A or B)) = 1 - P(A or B) = 1 - 17/20 = 3/20