MCQ

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

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#### 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(\[B\] )

Concept: Event - Mutually Exclusive Events

Is there an error in this question or solution?

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