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) 1/2
(b) 11/25
(c) 19/50
(d) none of these

Answer 1

(c) 19/50

Given:
P(A) = $\frac{1}{5}$
∴ P(A') = $1-\frac{1}{5}=\frac{4}{5}$
P(B) = $\frac{3}{10}$
∴ P(B') = $1-\frac{3}{10}=\frac{7}{30}$
Hence, required probability = P(A∩ B') + P(A'∩ B)
$$\begin{gathered} =\frac{1}{5}\times \frac{7}{10}+\frac{4}{5}\times \frac{3}{10} \\ =\frac{7}{50}+\frac{12}{50} \\ =\frac{19}{50} \end{gathered}$$