A problem in statistics is given to three students A , B and C . Their probabilities of solving the problem are 1 2 , 1 3 and 1 4 respectively, If all of them try independently, then the probability, that problem is solved, is

Step-by-step solution

aligned P ( A ) & = 1 2 P ( A ^ ) & =1- 1 2 = 1 2 P ( B ) & = 1 3 aligned array ll & P ( B ^ )=1- 1 3 = 2 3 & P ( C )= 1 4 & P ( C ^ )=1- 1 4 = 3 4 & P ( Problem is not solve ) & = P ( A ^ B ^ C ^ ) & = P ( A ^ ) P ( B ^ ) P ( C ^ ) & [ A ^ , B ^ , C ^ are independent ] array aligned & = 1 2 2 3 3 4 & = 1 4 aligned aligned & P(the problem will be solve) & =1- P (Problem is not solved) & =1- 1 4 & = 3 4 aligned