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 C

$\frac{19}{50}$

Given,

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

$\therefore P\left(A^{\prime }\right)1-\frac{1}{5}=\frac{4}{5}$

$P\left(B\right)=\frac{3}{10}$

$\therefore P\left(B^{\prime }\right)=1-\frac{3}{10}=\frac{7}{30}$

Hence, required probability

$=P(A\cap B^{\prime })+P(A^{\prime }\cap B)$

$=\frac{1}{5}\times \frac{7}{10}+\frac{4}{5}\times \frac{3}{10}$

$=\frac{7}{50}+\frac{12}{50}=\frac{19}{50}$