A problem in Mathematics is given to three students  $A, B, C$and their respective probability of solving  the problem are $\frac{1}{2},\frac{1}{3}$and $\frac{1}{4}$. Probability that the problem is solved, is 

Consider the following events: 

$E$= Student $A$solves the problem 

$F$= Student $B$solves the problem 

$G$= Student $C$solves the problem 

Clearly, $E,F,G$ are independent events such that

$P\left(E\right)=\frac{1}{2},P\left(F\right)=\frac{1}{3}$ and $P\left(G\right)=\frac{1}{4}$

Required probability  $=P(E\cup F\cup G)$

Required probability = $1-P\left(\overline{E}\right)P\left(\overline{F}\right)P\left(\overline{G}\right)$

Required probability = $=1-\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}=\frac{3}{4}$