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.

Step-by-step explanation:

Since we have given that

Probability of getting classroom 1 = $\dfrac{1}{2}$

Probability of getting classroom 2 = $\dfrac{1}{2}$

Probability of getting girl from classroom 1 = $\dfrac{13}{18}$

Probability of getting girl from classroom 2 = $\dfrac{9}{23}$

Using "Bayes theorem".

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

$\dfrac{\dfrac{1}{2}\times \dfrac{9}{23}}{\dfrac{1}{2}\times \dfrac{9}{23}+\dfrac{1}{2}\times \dfrac{13}{18}}\\\\=\dfrac{0.195}{0.195+0.361}\\\\=0.351$

Hence, our required probability is 0.351.