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Question
If A and B are mutually exclusive events then
Options
\[P\left( A \right) \leq P\left( B \right)\]
\[P\left( A \right) \geq P\left( B \right)\]
\[P\left( A \right) < P\left( B \right)\]
None of these
Solution
It is given that A and B are mutually exclusive events.
∴ P(A ∩ B) = 0 .....(1)
We know that,
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
⇒ P(A ∪ B) = P(A) + P(B) [From (1)]
⇒ P(A) + P(B) ≤ 1 [P(A ∪ B) ≤ 1]
⇒ P(A) ≤ 1 − P(B) = P( \[B\] )
∴ P(A) ≤ P(\[B\] )
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