The probabilities of solving a problem by students A, B and C independently are $\frac{1}{2}, \frac{1}{3}$, and $\frac{1}{4}$ respectively. If they start solving the given problem. independently, then the probability that atleast two of them will solve the problem successfully, is equal to

$\frac{7}{24}$

Probability that A and B can solve but ‘C’ is unable to solve

$=\frac{1}{2} . \frac{1}{3} . \frac{3}{4}=\frac{1}{8}$

Probability that A and C can solve but ‘B’ is unable to solve

$=\frac{1}{2} . \frac{2}{3} . \frac{1}{4}=\frac{1}{12}$

Probability that B and C can solve but ‘A’ is unable to solve

$=\frac{1}{2} . \frac{1}{3} . \frac{1}{4}=\frac{1}{24}$

Probability that all of them can solve the problem

$=\frac{1}{2} . \frac{1}{3} . \frac{1}{4}=\frac{1}{24}$

Thus required probability that atleast two of them can solve the problem

= $\frac{7}{24}$