Answer: Our required probability is 0.351.
Step-by-step explanation:
Since we have given that
Probability of getting classroom 1 = [tex]\dfrac{1}{2}[/tex]
Probability of getting classroom 2 = [tex]\dfrac{1}{2}[/tex]
Probability of getting girl from classroom 1 = [tex]\dfrac{13}{18}[/tex]
Probability of getting girl from classroom 2 = [tex]\dfrac{9}{23}[/tex]
Using "Bayes theorem".
so, the probability that classroom 2 was chosen given that a girl was chosen would be
[tex]\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[/tex]
Hence, our required probability is 0.351.
