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.

Question

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.

Doubtnut · Accepted Answer

Solution: Let `P(B_1)` and `P(B_2)` are the proababilities of seleting bag 1 and bag 2.
Let `P(R)` is the probability of drawing red ball.
Then, required probability can be given as,
`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))`
Here, `P(R/B_2) = 5/9`
`P(B_1) = P(B_2) = 1/2`
`P(R/B_1) =3/6 = 1/2`
Putting all these values,
`P(B_2/R) = (5/9*1/2)/(5/9*1/2+1/2*1/2) = (5/18)/(5/18+1/4)`
`=5/18*36/19 = 10/19`
So, the required probability is `10/19`.

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.