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Question

If A and B are two events of a random experiment, such that PA∪B=45,PA'∪B'=710, and P(B)=25, then the value of P(A) equals


A

910

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B

810

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C

710

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D

35

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Solution

The correct option is C

710


Step 1. Find the value of P(A∩B):

Given data,

PA∪B=45

P(A'UB')=710 and

P(B)=25

We know that,

P(A∩B)+P(A∩B)'=1....1

As P(A'UB')=P(A∩B)'

Equation 1 becomes

PAB=1-710=310

Step2 . Find the value of P(A)

We know that,

P(A)=PAB+P(AB)-PB; P(AUB)=P(A)+P(B)-P(AB)

=45+310-25

=710

∴P(A)=710

Hence, option "C"is correct.


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