Discussion Forum

Bag I contains 3 red and 4 black  balls , Bag II contains 5 red and 6 black balls .If one ball is drawn at random from one of the bags and it is found to be red , then the probability  that it was drawn from Bag II, is 

Answer:

Explanation:

Bag 1 contains 3 red and 4 black balls bag II  contains 5 red and 6 black balls

 P(I)=$\frac{1}{2}$,P(II)=$\frac{1}{2}$

$P\left(\frac{R}{I}\right)=\frac{3}{7}, P\left(\frac{R}{II}\right)=\frac{5}{11}$

$\therefore$ Required probability

$P\left(\frac{II}{R}\right)=\frac{P(II) \times P\left(\frac{R}{II}\right)}{P(I)\times P(R/I)+P(II)+P\left(\frac{R}{II}\right)}$

$=\frac{\frac{1}{2}\times \frac{5}{11}}{\frac{1}{2}\times\frac{3}{7}+\frac{1}{2}\times\frac{5}{11}}=\frac{35}{68}$