Question

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 they obtain the same answer, then the probability of their answer to be correct is ______.

Options

• `1/12`

• `1/40`

• `13/120`

• `10/13`

Answer 1

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 they obtain the same answer, then the probability of their answer to be correct is `10/13`.

Explanation:

Let E₁ be the event that both of them solve the problem.

∴ P(E₁) = `1/3 xx 1/4 = 1/12`

And E₂ be the event that both of them same incorrectly the problem.

∴ P(E₂) = `(1 - 1/3) xx (1 - 1/4)`

= `2/3 xx 3/4 = 1/2`

Let H be the event that both of them get the same answer.

Here, `"P"("H"/"E"_1)` = 1

`"P"("H"/"E"_2) = 1/20`

∴ `"P"("E"_1/"H") = ("P"("E"_1)*"P"("H"/"E"_1))/("P"("E"_1)*"P"("H"/"E"_1) + "P"("E"_2)*"P"("H"/"E"_2))`

= `(1/12 xx 1)/(1/12 xx 1 + 1/2 xx 1/20)`

= `(1/12)/(1/12 + 1/40)`

= `(1/12)/((10 + 3)/120)`

= `(1/12)/(13/120)`

= `10/13`