Question

If A and B are two events in a sample space such that $P\left(A\right)=\frac{2}{5},P\left(B\right)=\frac{1}{2}$
and $P(A\cup B)=\frac{3}{5},findP(A\cap B).$

• A. $\frac{3}{10}$
• B. $\frac{7}{10}$
• C. $\frac{4}{7}$
• D. $\frac{4}{15}$

Answer 1

The correct option is A $\frac{3}{10}$

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)\frac{3}{5}=\frac{2}{5}+\frac{1}{2}-P(A\cap B)\Rightarrow P(A\cap B)=\frac{3}{10}$