A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

Let A, B, C be the respective events of solving the problem and  $A , B, C$ be the respective events of not solving the problem. Then A, B, C are independent event

$\therefore A, B, C$ are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

  $PA=\frac{1}{2}, PB=\frac{2}{3}, PC= \frac{3}{4}$

$\therefore$ P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  =  $PA\cap B\cap C$ 

                  =  $PAPBPC$          $\because A, B, C are Independent$                       

                  =   $\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}$  

                  =  $\frac{1}{4}$  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                =  $1-\frac{1}{4}$= 3/4