Urn a contains 2 red and 4 white balls, and urn b contains 1 red and 1 white ball. a ball is randomly chosen from urn a and put into urn b, and a ball is then chosen from urn b. what is the conditional probability that the transferred ball was white given that a white ball is selected from urn b?

0.7991

Step-by-step explanation:

Given : Urn A contains 2 red and 4 white balls, and urn B contains 1 red and 1 white ball.

Let be the event that the transferred ball was white.

and be the event that the ball drawn from urn B was white.

Then by Bayes theorem, the conditional probability that the transferred ball was white given that a white ball is selected from urn B will be :-

Where,

[ by conditional probability formula]

[By law of total probability]

i.e.

Now,

Hence, the required probability =0.7991

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