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

Answer 1

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(\[B\] )