# 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 - Mathematics and Statistics

Sum

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?

#### 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

Concept: Baye'S Theorem
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (17) | Page 214