If $A\ and\ B$ are two events such that $P(A \cup B) = \frac{5}{6}$, $P(A \cap B) = \frac{1}{3}and\ P\left( \overline{B} \right) = \frac{1}{3}$,then the value of $P(A)$is

Question

Dr. Abubacker · Accepted Answer

(c)
Given, $P\left( \overline{B} \right) = \frac{1}{3} \Rightarrow P(B) = \frac{2}{3}$,
$P(A \cup B) = \frac{5}{6},P(A \cap B) = \frac{1}{3}$
Now, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow \frac{5}{6} = P(A) + \frac{2}{3} - \frac{1}{3}$
$\Rightarrow P(A) = \frac{5}{6} - \frac{2}{3} + \frac{1}{3} = \frac{1}{2}$

Q. If $A\ and\ B$ are two events such that $P(A \cup B) = \frac{5}{6}$, $P(A \cap B) = \frac{1}{3}and\ P\left( \overline{B} \right) = \frac{1}{3}$,then the value of $P(A)$is

Explanation

Reviewed by Dr. Abubacker

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