SOLUTION: 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 Then a ball is withdrawn from the chosen urn.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

Algebra ->  Probability-and-statistics -> SOLUTION: 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 Then a ball is withdrawn from the chosen urn.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      Log On


   

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 Then a ball is withdrawn from the chosen urn.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(13367) About Me  (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