SOLUTION: Please help me on this question. Thanks! Two urns contain white and black balls. Urn 1 contains 3 white balls and 4 black balls. Urn 2 contains 5 white and 3 black balls. It is t

Algebra ->  Probability-and-statistics -> SOLUTION: Please help me on this question. Thanks! Two urns contain white and black balls. Urn 1 contains 3 white balls and 4 black balls. Urn 2 contains 5 white and 3 black balls. It is t      Log On


   

Question 1183552: Please help me on this question. Thanks!
Two urns contain white and black balls. Urn 1 contains 3 white balls and 4 black balls. Urn 2 contains 5 white and 3 black balls. It is three times as likely to draw a ball from Urn 1 as it is from Urn 2. Blindfolded, you draw a ball randomly from one of the two urns. The ball drawn is then put inside a third urn which contains 2 white and 3 black balls.
a) What is the probability of drawing a black ball from the third urn?
b) What is the probability that a black ball drawn from the third urn came from Urn 2?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Again this problem should be EASY application of the law of total probability and Bayes' theorem.
The solution to this problem is very similar to the one I gave earlier. The only difference being, in the first problem, P%28U1%29=+1%2F2 and P%28U2%29+=+1%2F2,
but for this problem, P%28U1%29+=+3%2F4 and P%28U2%29+=+1%2F4.
Fill in the corresponding probabilities for the formula I included in the first problem.