Question

If $P\left(A\right)=\frac{3}{4},P\left(B^{\prime }\right)=\frac{1}{3}andP(A\cap B)=\frac{1}{2}$ then find $P(A\cup B)$.

• A. $\frac{5}{12}$
• B. $\frac{6}{12}$
• C. $\frac{7}{12}$
• D. $\frac{11}{12}$

Answer 1

Answer: (D)

$\frac{11}{12}$

Given that:

$P\left(A\right)=\frac{3}{4},P\left(B^{\prime }\right)=\frac{1}{3}$ and $P(A\cap B)=\frac{1}{2}$

To Find:

$P(A\cup B)=?$

Solution:

$P\left(B\right)=1-P\left(B^{\prime }\right)=1-\frac{1}{3}=\frac{2}{3}$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{3}{4}+\frac{2}{3}-\frac{1}{2}$

$=\frac{11}{12}$

Hence, D is the correct option.