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Question: If \(P ( A ) = 0.4 , P ( B ) = x , P ( A \cup B ) = 0.7\) and the events A and B are mutually exclu...

If P(A)=0.4,P(B)=x,P(A∪B)=0.7P ( A ) = 0.4 , P ( B ) = x , P ( A \cup B ) = 0.7 and the events A and B are mutually exclusive, then x=x =

A

310\frac { 3 } { 10 }

B

12\frac { 1 } { 2 }

C

25\frac { 2 } { 5 }

D

15\frac { 1 } { 5 }

Answer

310\frac { 3 } { 10 }

Explanation

Solution

Since events are mutually exclusive, therefore

P(AB)=0P ( A B ) = 0 i.e., P(A∪B)=P(A)+P(B)P ( A \cup B ) = P ( A ) + P ( B )

⇒0.7=0.4+x⇒x=310\Rightarrow 0.7 = 0.4 + x \Rightarrow x = \frac { 3 } { 10 }