Question
Let there be three urns containing 1 white, 2 black, 3 red balls ; 2 white, 1 black, 1 red ball ; 4 white, 5 black, 3 red balls. One urn is chosen at random and two balls are drawn. These happen to be white and a red. What is the probability that they come from urn number 3.
Solution
Let E1 , E2, E3 be events of selecting urns I, II, III respectively.
White Black Red
Urn I: 1 2 3
Urn II: 2 1 1
Urn III: 4 5 3
White Black Red
Urn I: 1 2 3
Urn II: 2 1 1
Urn III: 4 5 3
Let A be the event that the drawn balls are, one red and one white.
Since, the urns are equally likely
∴ P( A/E1) = Probability that one red and one white ball are drawn from first urn
