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प्रश्न
If A and B are mutually exclusive events, then ______.
पर्याय
`P(A) ≤ P(barB)`
`P(A) ≥ P(barB)`
`P(A) < P(barB)`
None of these
उत्तर
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)`
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