Question

If three students A, B, C independently solve a problem with probabilities $\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$ respectively, then the probability that the problem will be solved is

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{2}{5}$
• D. $\frac{47}{60}$

Answer 1

The correct option is A $\frac{3}{5}$

Required probability $=1-\underset{\text{when none them solved the problem}}{\underset{}{(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{3})}}$

$=1-\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}=\frac{3}{5}$