Refer to Question 41 above. If a white ball is selected, what is the probability that it came from
(i) Bag 2 (ii) Bag 3
Referring to the previous question, using Bayes theorem, we get
Let E1, E2, and E3 be the events that Bag 1, Bag 2 and Bag 3 is selected, and a ball is chosen from it.
Bag 1: 3 red balls,
Bag 2: 2 red balls and 1 white ball
Bag 3: 3 white balls.
The probability that bag i will be chosen and a ball is selected from it is i|6.
Let F be the event that a white ball is selected. Therefore, is the probability that white ball is chosen from the bag 1 .
is the probability that white ball is chosen from the bag 2 .
To find: the probability that if white ball is selected, it is selected from:
(i) Bag 2
Using Bayes’ theorem to find the probability of occurrence of an event A when event B has already occurred.
(ii)Bag 3
Using Bayes' theorem to find the probability of occurrence of an event A when event B has already occurred.
Using Bayes' theorem, we get the probability of as: