Question

For two independent events $A$ and $B$, what is $P(A+B)$, given $P\left(A\right)=\frac{3}{5}$ and $P\left(B\right)=\frac{2}{3}$?

• A. $\frac{11}{15}$
• B. $\frac{13}{15}$
• C. $\frac{7}{15}$
  
• D. $0.65$

Answer 1

The correct option is B $\frac{13}{15}$

Given: $P\left(A\right)=\frac{3}{5},P\left(B\right)=\frac{2}{3}$, $A$ and $B$ are independent.

To find: $P(A+B)=?$

Sol: As $A$ and $B$ are independent, $P(A\cap B)=P\left(A\right)P\left(B\right)$

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

$⟹P(A+B)=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)⟹P(A+B)=\frac{3}{5}+\frac{2}{3}-\frac{3}{5}\times \frac{2}{3}⟹=\frac{10+9-6}{15}=\frac{13}{15}$