SOLUTION: Box A contains 6 red and 7 yellow balls while box B contains 5 red and 3 yellow balls. A box is chosen at random and a ball is selected from it. The probability of choosing box A i

Algebra ->  Probability-and-statistics -> SOLUTION: Box A contains 6 red and 7 yellow balls while box B contains 5 red and 3 yellow balls. A box is chosen at random and a ball is selected from it. The probability of choosing box A i      Log On


   



Question 384295: Box A contains 6 red and 7 yellow balls while box B contains 5 red and 3 yellow balls. A box is chosen at random and a ball is selected from it. The probability of choosing box A is 58%. Find the the probability that the ball came from box A if the ball was yellow.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P(A|Y) = P(AY)/P(Y) = (P(Y|A)*P(A))/(P(Y|A)*P(A)) + P(Y|B)*P(B)) =
%287%2F13%29%2A0.58%2F%28%287%2F13%29%2A0.58+%2B+%283%2F8%29%2A0.42%29+=+0.6648. This is by direct use of Bayes' Theorem.