A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem is solved is

3/4

The correct answer is Option (1) → 3/4 **

Let the probabilities of solving the problem be:

$P_{1}=\frac{1}{2},\; P_{2}=\frac{1}{3},\; P_{3}=\frac{1}{4}$

Probability that none of them solves:

$\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)$

$=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}$

$=\frac{1}{4}$

Therefore probability that at least one solves:

$1-\frac{1}{4}=\frac{3}{4}$

The required probability is $\frac{3}{4}$.