`A` and `B` are two students. Their chances of solving a problem correctly are `1/3` and `1/4`, respectively If the probability of their making a common error is, `1/20` and the obtain the same answer, then the probability of their answer to be correct is

Explanation

Let, `E_1 =` Both `A` and `B` solved problem.


`E_2 =` Both `A` and `B` got wrong answer.


`E =` Both `A` and `B` got same answer of question.



Given,


`P(E_1)=1/3*1/4=1/12`


`P(E_2)=2/3*3/4=1/2`


`P(E//E_1)=1, P(E//E_2)=1/20`



Using bayes theorem,


...