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Question
Solve the following:
The ratio of Boys to Girls in a college is 3:2 and 3 girls out of 500 and 2 boys out of 50 of that college are good singers. A good singer is chosen what is the probability that the chosen singer is a girl?
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Solution
Let event S: Student is a good singer,
event B: Student is a boy,
event G: Student is a girl.
Since the ratio of boys to girls is 3:2 and
3 girls out of 500 and 2 boys out of 50 are good singers.
∴ P(B) = `3/5`, P(G) = `2/5`, `"P"("S"/"G") = 3/500`, `"P"("S"/"B") = 2/50`.
`"P"("S") = "P"("G") xx "P"("S"/"G") + "P"("B") xx "P"("S"/"B")`
= `2/5 xx 3/500 + 3/5 xx 2/50`
= `(2xx3)/5(1/500+1/50)`
= `6/5 xx 11/500`
= `33/1250`
Required probability = `"P"("G"/"S")`
By Bayes’ theorem,
`"P"("G"/"S") = ("P"("G") "P"("S"/"G"))/("P"("S")`
= `(2/5 xx 3/500)/(33/1250)`
= `1/11`
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