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Question
Solve the following:
The chances of P, Q and R, getting selected as principal of a college are `2/5, 2/5, 1/5` respectively. Their chances of introducing IT in the college are `1/2, 1/3, 1/4` respectively. Find the probability that IT is introduced in the college after one of them is selected as a principal
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Solution
Let event P: P become principal.
event Q: Q become principal.
event R: R become principal.
event E: Subject IT is introduced.
Given, `"P"("P") = 2/5, "P"("Q") = 2/5, "P"("R") = 1/5`
and `"P"("E"/"P") = 1/2, "P"("E"/"Q") = 1/3`,
`"P"("E"/"R") = 1/4`
Required probability = P(E)
= `"P"("P") * "P"("E"/"P") + "P"("Q") * "P"("E"/"Q") + "P"("R") * "P"("E"/"R")`
= `2/5 xx 1/2 + 2/5 xx 1/3 + 1/5 xx 1/4`
= `1/5 + 2/15 + 1/20`
= `(12 + 8 + 3)/60`
= `23/60`
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