A problem in Mathematics is given to two students X and Y whose chances of solving it are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that only X solves the problem, is:

$\frac{1}{4}$

The correct answer is Option (3) → $\frac{1}{4}$

$P(X)=\frac{1}{3},\;P(Y)=\frac{1}{4}$

$P(\text{only X solves})=P(X)\bigl(1-P(Y)\bigr)$

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

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

$=\frac{1}{4}$

The probability that only X solves the problem is $\frac{1}{4}$.