Given that events A and B are such that P(A)=frac{1}{2}, P(A cup B)=frac{3}{5} and P(B)=p . Find p i

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14.Probability

easy

Given that the events $A$ and $B$ are such that $P(A)=\frac{1}{2}, P(A \cup B)=\frac{3}{5}$ and $P(B)=p .$ Find $p$ if they are independent.

A

$\frac{1}{5}$

B

$\frac{1}{5}$

C

$\frac{1}{5}$

D

$\frac{1}{5}$

Solution

When $A$ and $B$ are independent, $P(A \cap B)=P(A) P(B)=\frac{1}{2} p$

It is known that, $P(A \cup B)=P(A)+P(B)-P(A \cap B)$ $\Rightarrow \frac{3}{5}=\frac{1}{2}+p-\frac{1}{2} p$

$\Rightarrow \frac{3}{5}=\frac{1}{2}+\frac{p}{2}$

$\Rightarrow \frac{p}{2}=\frac{3}{5}-\frac{1}{2}=\frac{1}{10}$

$\Rightarrow p=\frac{2}{10}=\frac{1}{5}$

Standard 11

Mathematics

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