There are two bags I and II. Bag I contains 3 white and 3 red balls and Bag II contains 4 white and 5 redballs. One ball is drawn at random from one of the bags and is found to bered. Find the probability that it was drawn from bag II. Question from Class 12 Chapter Board Paper SolutionsApne doubts clear karein ab Whatsapp par bhi. Try it now. Let `P(B_1)` and `P(B_2)` are the proababilities of seleting bag 1 and bag 2.<br>Let `P(R)` is the probability of drawing red ball.<br>Then, required probability can be given as,<br>`P(B_2/R) = (P(R/B_2)P(B_2))/(P(R/B_2)P(B_2)+P(R/B_1)P(B_1))`<br>Here, `P(R/B_2) = 5/9`<br>`P(B_1) = P(B_2) = 1/2`<br>`P(R/B_1) =3/6 = 1/2`<br>Putting all these values,<br>`P(B_2/R) = (5/9*1/2)/(5/9*1/2+1/2*1/2) = (5/18)/(5/18+1/4)`<br>`=5/18*36/19 = 10/19`<br>So, the required probability is `10/19`.<br>