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Question
If E1 and E2 are equally likely, mutually exclusive and exhaustive events and `"P"("A"/"E"_1 )` = 0.2, `"P"("A"/"E"_2)` = 0.3. Find `"P"("E"_1/"A")`
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Solution
E1, E2 are equally likely, mutually exclusive and exhaustive events
∴ P(E1) = P(E2) = `1/2`
It is given that `"P"("A"/"E"_1 )` = 0.2, `"P"("A"/"E"_2)` = 0.3
By Baye's Theorem,
`"P"("E"_1/"A") = ("P"("E"_1)*"P"("A"/"E"_1))/("P"("E"_1)*"P"("A"/"E"_1) + "P"("E"_2)*"P"("A"/"E"_2)`
= `(1/2 xx 0.2)/(1/2 xx 0.2 + 1/2 xx 0.3)`
= `(0.2)/(0.5)`
= `2/5`
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