If $P(A) = P(B) = x\ and\ P(A \cap B) = P\left( A^{'} \cap B^{'} \right) = \frac{1}{3}$, then $x$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
$P\left( A^{'} \cap B^{'} ight) = 1 - P(A \cup B) = \frac{1}{3}$ [given]
$\Rightarrow \ P(A \cup B) = \frac{2}{3}$
$	herefore\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow \ \frac{2}{3} = x + x - \frac{1}{3}\  \Rightarrow \ x = \frac{1}{2}$

Q. If $P(A) = P(B) = x\ and\ P(A \cap B) = P\left( A^{'} \cap B^{'} \right) = \frac{1}{3}$, then $x$ is equal to

Explanation

Reviewed by Dr. Abubacker

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