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

? A , B , C are independent events

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

  P A = 1 2 , P B = 2 3 , P C = 3 4

? P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  =  P A ? B ? C 

                  =  P A P B P C          ? A , B , C a r e I n d e p e n d e n t                       

                  =   1 2 × 2 3 × 3 4  

                  =  1 4  

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

                =  1 - 1 4= 3/4