Let A = first student solve the problem
B = 2nd student solve the problem
C = 3rd student solve the problem
then
\(P(A)=\frac{1}{3}, P\left(A^{\prime}\right)=1-\frac{1}{3}=\frac{2}{3}, P(B)=\frac{1}{4},\left(B^{\prime}\right)=1-\frac{1}{4}=\frac{3}{4}\)
\(P(C)=\frac{1}{5}, P\left(C^{\prime}\right)=1-\frac{1}{5}=\frac{4}{5}\)
Let E = the problem will be solved.
then \(P(E)=P(A \cup B \cup C)=1-P\left(A^{\prime}\right) \cdot P\left(B^{\prime}\right) \cdot P\left(C^{\prime}\right)\)
\(=1-\frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5}=1-\frac{2}{5}=\frac{3}{5}\)