NIELIT 2018-26

Question

If $P(A \cap B) = \frac{1}{2}, \: P(\overline{A} \cap \overline{B}) = \frac{1}{2}$ and $2P(A)=P(B)=p$, then the value of $p$ is given by:

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{2}{3}$

Comments

continuing previous comment

$\frac{1}{2}=\;1-P(A\cup B)$

$\frac{1}{2}=\;1- [\;P(A) + \;P(B)-P(A\cap B)] $

$\frac{1}{2}=\;1- [\;\frac{p}{2} + \;p-\frac{1}{2}] $

$1=2-[3p-1] $

$1=2-3p+1 $

$3p=2 ===> p=\frac{2}{3}$

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feeling stupid now :p

thanks

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Don't worry brother

Sometimes I also did:)