There are two bags I and II.
Bag I contains 3 white and 3 red balls and Bag II contains 4 white and 5 red
balls. One ball is drawn at random from one of the bags and is found to be
red. Find the probability that it was drawn from bag II.
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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>