Question

There are 4 boys and 2 girls in Room no. 1 and 5 boys and 3 girls in room no 2 Find the probability that a girl from one of the two rooms laughed loudly was from Room no. 2?

Answer 1

Consider the problem,

The probability that girl laugh from room 1 is:

$\begin{array}{c}P\left(E_1\right)=\frac{1}{2}\\ P\left(E_2\right)=\frac{1}{2}\\ P\left(E_1/G\right)=\frac{2}{6}\\ P\left(E_2/G\right)=\frac{3}{8}\\ ApplytheBay{e}^{\prime }stheorem\\ P\left(G/E_2\right)=\frac{\frac{1}{2}\left(\frac{3}{8}\right)}{\frac{1}{2}\left(\frac{2}{6}\right)+\frac{1}{2}\left(\frac{3}{8}\right)}=\frac{9}{17}\end{array}$