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  4. Let A and B be two events such that P(A)=0.3 and P(A ∪ B)=0.8. If A and B are independent events. Then, P(B) is equal to

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Q. Let $A$ and $B$ be two events such that $P(A)=0.3$ and $P(A \cup B)=0.8$. If $A$ and $B$ are independent events. Then, $P(B)$ is equal to

Bihar CECEBihar CECE 2011

Solution:

Let $P(B)=b$, then we have
$P(A \cup B)=P(A)+P(B)-P(A) \cdot P(B)$
(Since $A$ and $B$ are independent events.)
$\therefore 0.8=0.3+b-0.3 \times b$
$ \Rightarrow b=5 / 7$