Question

If A and B are the two events of a sample space such that $P(A\cup B)=\frac{5}{6}$, $P(A\cap B)=\frac{1}{3}$, $P\left(B\right)=\frac{1}{3}$. Find P(A)

• A. $\frac{1}{6}$
• B. $\frac{2}{6}$
• C. $\frac{4}{6}$
• D. $\frac{5}{6}$

Answer 1

The correct option is D $\frac{5}{6}$

$P(A\cup B)=\frac{5}{6}$, $P(A\cap B)=\frac{1}{3}$, $P\left(B\right)=\frac{1}{3}$
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\frac{5}{6}=P\left(A\right)+\frac{1}{3}-\frac{1}{3}$

$-P\left(A\right)=\frac{1}{3}-\frac{1}{3}-\frac{5}{6}$

$-P\left(A\right)=-\frac{5}{6}$
$P\left(A\right)=\frac{5}{6}$