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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`
Solution
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`
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