Question

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35.

Find

1. P(A ∪ B)
2. P(A′ ∩ B′)
3. P(A ∩ B′)
4. P(B ∩ A′)

Answer 1

1. P(A) = 0.54, P(B) = 0.69, P(A ∩ B) = 0.35
   P(A ∪ B) = P(A) + P(B) – (A ∩ B)
   = 0.54 + 0.69 – 0.35
   = 0.88
2. P(A’ ∩ B’) = P[(A ∪ B)’] = 1 – P(A ∪ B)
   1 – 0.88
   = 0.12
3. P(A ∩ B’) = P(A) – P(A ∩ B)
   0.54 – 0.35
   = 0.19
4. P(B ∩ A’) = P(B) – P(B ∩ A)
   = 0.69 – 0.35
   = 0.34