Question

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?
A) 1/4
B) 1/2
C) 3/4
D) 7/12

Answer 1

$\bf\huge\color{red}{SOLUTION;}$

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

∴A, B, C∴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)PAPBPC         [∵ A, B, C are Independent]∵ A, B, C are Independent                       

                  =  12×23×3412×23×34  

                  = 1414  

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

                = 1−141-14= 3/4