Question
Two events A and B will be independent, if
- A and B are mutually exclusive
- P(A'B') = [1 - P(A)] [1 - P(B)]
- P(A) = P(B)
- P(A) + P(B) = 1
Solution
B.
P(A'B') = [1 - P(A)] [1 - P(B)] P(A'B') = (P(A' ∩ B') = P(A ∪ B)'
= 1 - P(A ∪ B)
= 1 - [P(A) + P(B) - P(A ∩ B)]
= 1 - P(A) - P(B) + P(A ∩ B)
= 1 - P(A) - P(B) + P(A) P(B) [A and B are independent]
= [1 - P(A)] [1 - P(B)]
∴ (B) is correct answer.
