Question 1201946: One of two urns is chosen at random with one just as likely to be chosen as the other. Then a ball is withdrawn from the chosen urn. Urn 1 contains 1 white and 5 red balls, and urn 2 has 5 white and 2 red balls.
If a white ball is drawn, what is the probability that it came from urn 1?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) Find the probabilities that a white is selected from either urn
P(urn 1, white) = (1/2)(1/6) = 1/12
P(urn 2, white) = (1/2)(5/7) = 5/14
(2) Add those two probabilities to find the overall probability that a white is selected
P(white) = 1/12 + 5/14 = 7/84 + 30/84 = 37/84
(3) Calculate the conditional probability that the ball came from urn 1, given that it is white
P(urn 1 | white) = (1/12)/(37/84) = (7/84)(37/84) = 7/37
ANSWER: 7/37
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