Question

If A and B are two mutually exclusive events, then which one of the following is true?
1. P(A) ≤ P(B̅)
2. P(A ∪ B) = P(A ∩ B)
3. P(A) - P(B) = P(A̅ ) - P(B̅)
4. P(A ∪ B) = P(A̅ ∪ B̅) 

Answer 1

Correct Answer - Option 1 : P(A) ≤ P(B̅)

Concept:

Probability ≤ 1

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

For mutually exclusive events A and B, P(A ∩ B) = 0

P(B̅) = 1 - P(B)

 

Calculation:

We know, for mutually exclusive events A and B,  P(A ∩ B) = 0

P(B̅) = 1 - P(B)

P(A ∪ B) ≤ 1

P(A) + P(B) ≤ 1

P(A) ≤ 1 - P(B)

P(A) ≤ P(B̅)

Hence, option (1) is correct.