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# If a and B Are Mutually Exclusive Events Then (A) P ( a ) ≤ P ( B ) (B) P ( a ) ≥ P ( B )(C) P ( a ) < P ( B ) (D) None of These - Mathematics

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($B$ )

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Q 34 | Page 73
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