Question

If A and B are mutually exclusive events, then ______.

Options

• `P(A) ≤  P(barB)`

• `P(A) ≥ P(barB)`

• `P(A) < P(barB)`

• None of these

Answer 1

If A and B are mutually exclusive events, then `P(A) ≤  P(barB)`.

Explanation:

For mutually exclusive events,

P(A ∩ B) = 0

∴ P(A ∪ B) = P(A) + P(B)   .....[∵ P(A ∩ B) = 0]

⇒ P(A) + P(B) ≤ 1

⇒ `P(A) + 1  –  P(barB) ≤ 1`   .....`[P(B) = 1 - P(barB) = 0]`

⇒ `P(A)  –  P(B) ≤ 0`

⇒ `P(A) ≤ P(barB)`