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Question: If A and B are two events such that \(P ( A ) = 0.4\) , \(P ( A + B ) = 0.7\) and \(P ( A B ) = 0...

If A and B are two events such that P(A)=0.4P ( A ) = 0.4 ,

P(A+B)=0.7P ( A + B ) = 0.7 and P(AB)=0.2P ( A B ) = 0.2 then P(B)=P ( B ) =

A

0.1

B

0.3

C

0.5

D

None of these

Answer

0.5

Explanation

Solution

Since we have P(A+B)=P(A)+P(B)−P(AB)P ( A + B ) = P ( A ) + P ( B ) - P ( A B )

⇒0.7=0.4+P(B)−0.2⇒P(B)=0.5\Rightarrow 0.7 = 0.4 + P ( B ) - 0.2 \Rightarrow P ( B ) = 0.5.