Question

Data on readership of a magazine indicates that the proportion of male readers over 30 years old is 0.30 and the proportion of male readers under 30 is 0.20. If the proportion of readers under 30 is 0.80. What is the probability that a randomly selected male subscriber is under 30?

Answer 1

Let E₁ be the event of the subscriber is under 30 and E₂ be the event of the subscriber is above 30.

Let B be the event of the subscriber is a male.

Given P(E₁) = 0.80 and P(E₂) = 1 − 0.8 = 0.2

and P`("B"/"E"_1)` = 20, P`("B"/"E"_2)` = 0.30

∴ `"P"("E"_1/"B") = ("P"("E"_1) xx "P"("B"/"E"_1))/("P"("E"_1) xx "P"("B"/"E"_1) + "P"("E"_2) xx "P"("B"/"E"_2))`

= `(0.80 xx 0.20)/(0.80 xx 0.20 + 0.20 xx 0.30)`

= `0.16/(0.16 + 0.06)`

= `0.16/0.22`

= `16/22`

∴ `"P"("E"_1/"B")` = 0.727