NIMCET 2013 Question Paper with solutions

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Question : 34 of 120

Marks: +1, -0

If A and B are two events such that P (A ∪ B) =

5/6

, P (A ∩ B) =

1/3

and P (

B↖{-}

) =

1/2

, then the events A and B are :

Depedent
Independent
Mutually exclusive
None of these

Solution:

Given,

P(A∪B)=5/6

P(A∩B)=1/3

and

P(B)=1/2

Now,

P(A∪B)=P(A)+P(B)-P(A∩B)

⇒5/6=P(A)+1/2-1/3

⇒P(A)=4/6=2/3

So,

P(A)⋅P(B)=P(A∩B)

∴ Events are independent

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