A problem in mathematics is given to three students \(A, B\) and \(C\) whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. If they all try to solve the problem, what is the probability that the problem will be solved?
\(\quad P(\mathrm{~A})=\frac{1}{2}, P(B)=\frac{1}{3}\) and \(P(C)=\frac{1}{4}\) Problem will be solved if any one of them can solve the problem \[\] \(\therefore P(A \cup B \cup C)=1-P(\bar{A})+P(\bar{B})+P(\bar{C})\) \[\] \(=1-\frac{1}{2} \times \frac{1}{4} \times \frac{3}{4}=1-\frac{1}{4}=\frac{3}{4}\) \[\] Choice (D)\[\]
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