Question

If the probability of $A$ to fail in an examination is $\frac{1}{5}$ and that of $B$ is $\frac{3}{10}$ then the probability that either $A$ or $B$ fails is

• A. $\frac{1}{2}$
• B. $\frac{11}{25}$
• C. $\frac{19}{50}$
• D. none of these

Answer 1

The correct option is B $\frac{11}{25}$

Let E be the event that either A or B fails.Also let $A^F$ and $B^F$ be the event of failure of A and B respectively.
Then $P\left(E\right)=P(A^F\cup B^F)=P\left(A^F\right)+P\left(B^F\right)-P(A^F\cap B^F)\Rightarrow P\left(E\right)=\frac{1}{5}+\frac{3}{10}-(\frac{1}{5}\times \frac{3}{10})$
since the failing of A and B are independent.
$\Rightarrow P\left(E\right)=\frac{10+15-3}{50}=\frac{22}{50}=\frac{11}{25}$