Question

Three persons work independently on a problem. If the respective probabilities that they will solve it are $1/3,1/4$ and $1/5$, then find the probability that none can solve it.

• A. $\frac{3}{5}$
• B. $\frac{2}{5}$
• C. $\frac{1}{5}$
• D. $0$

Answer 1

Answer: (B)

$\frac{2}{5}$

Given events are independent
$\therefore$ Required probability is
$(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})=\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}=\frac{2}{5}$