Question

One of two small classrooms is chosen at random with equally likely probability, and then a student is chosen at random from the chosen classroom.

Classroom #1 has 5 boys and 13 girls.
Classroom #2 has 14 boys and 9 girls.

What is the probability that Classroom #2 was chosen at random, given that a girl was chosen?

Answer 1

Answer: Our required probability is 0.351.

Explanation:

Since we have given that

Probability of getting classroom 1 =
`(1)/(2)`

Probability of getting classroom 2 =
`(1)/(2)`

Probability of getting girl from classroom 1 =
`(13)/(18)`

Probability of getting girl from classroom 2 =
`(9)/(23)`

Using "Bayes theorem".

so, the probability that classroom 2 was chosen given that a girl was chosen would be

`((1)/(2)* (9)/(23))/((1)/(2)* (9)/(23)+(1)/(2)* (13)/(18))\\\\=(0.195)/(0.195+0.361)\\\\=0.351`

Hence, our required probability is 0.351.