A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3, and 1/4. Probability that the problem is solved is

$\begin{array}{l}\mathrm{P}\left(\mathrm{A}\right)=\frac{1}{2},\mathrm{P}\left(\mathrm{B}\right)=\frac{1}{3},\text{ and }\mathrm{P}\left(\mathrm{C}\right)=\frac{1}{4}\\ \therefore \mathrm{P}\left(\overline{\mathrm{A}}\right)=1-\frac{1}{2}=\frac{1}{2},\mathrm{P}\left(\overline{\mathrm{B}}\right)=1-\frac{1}{3}=\frac{2}{3}\\ \mathrm{P}\left(\overline{\mathrm{C}}\right)=1-\frac{1}{4}=\frac{3}{4}\end{array}$

Therefore, the required probability is=1-P(problem not solved)

$\begin{array}{c}\Rightarrow 1-P(\overline{A}\cap \overline{B}\cap \overline{C})=1-\mathrm{P}\left(\overline{\mathrm{A}}\right)\mathrm{P}\left(\overline{\mathrm{B}}\right)\mathrm{P}\left(\overline{\mathrm{C}}\right)=1-\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\\ =1-\frac{1}{4}=\frac{3}{4}\end{array}$