SOLUTION: (By way of conditional probability) Urn A contains 2 white and 4 red balls, whereas urn B contains 1 white and 1 red ball. A ball is randomly chosen from urn A and put in urn B, a

Question 258378: (By way of conditional probability)
Urn A contains 2 white and 4 red balls, whereas urn B contains 1 white and 1 red ball. A ball is randomly chosen from urn A and put in urn B, and a ball is then randomly selected from urn B.
(a) What is the probability that the ball selected from urn B is white?
(b) What is the conditional probability that the transferred ball was white given that a white ball is selected from urn B?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
There are 3 balls in B.
1/3 of the time they are wwr and 2/3 of the time they are rrw.
a) There are 4 possibilities:
1/3 * 2/3 = 2/9 w
1/3 * 1/3 = 1/9 r
2/3 * 1/3 = 2/9 w
2/3 * 2/3 = 4/9 r
.
2/9+2/9=49 w
.
b)
We select a white ball from B. Is it the transferred ball or the ball originally in B?
Now our sample space is restricted to the 2/9 where a white ball is transferred and chosen and 2/9 where it was not transferred and chosen.
So only the half where the w ball was transferred is a possibility and the chance of selecting it is 1/2.
1/2 * 1/2 = 1/4 the conditional probability that the transferred ball was white given that a white ball is selected from urn B.
.
Ed
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