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

Correct option is B

​$$\text{let } A, B, C \text{ be events of solving problem} \\\bar{A}, \bar{B}, \bar{C} \text{ be events of not solving problem} \\P(A) = \frac{1}{2}, \quad P(B) = \frac{1}{3}, \quad P(C) = \frac{1}{4} \quad (\text{since } P(A) + P(\bar{A}) = 1) \\\therefore P(\bar{A}) = \frac{1}{2} P(\bar{B}) = \frac{2}{3} P(\bar{C}) = \frac{3}{4} \\P(\text{problem is solved}) = 1 - P(\text{no one solves the problem}) \\= 1 - \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \\= 1 - \frac{1}{4} \\P(\text{Problem will be solved}) = \frac{3}{4}$$​​