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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(\[B\] ) 

 

 

  Is there an error in this question or solution?
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APPEARS IN

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