SOLUTION: An urn contains 14 balls; 6 of them are white, and the others are black. Another urn contains 9 balls; 3 are white, and 6 are black. A ball is drawn at random from the first urn

Question 360608: An urn contains 14 balls; 6 of them are white, and the others are black. Another urn contains 9 balls; 3 are white, and 6 are black. A ball is drawn at random from the first urn and is placed in the second urn. Then, a ball is drawn at random from the second urn. If this ball is white, find the probability that the ball drawn from the first urn was black.
**Well, I know that I have to use the Law of Total Probability and the Bayes'Rule but I don't understand how.
So much thanks
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let b1 = event that 1st ball drawn is black,
w1 = event that 1st ball drawn is white,
b2 = event that 2nd ball drawn is black,
w2 = event that 2nd ball drawn is white.
Then P(b1|w2) = P(b1 and w2)/P(w2)= P(b1 and w2)/[P(b1 and w2)+P(w1 and w2)]
=P(w2|b1)*P(b1)/[P(w2|b1)*P(b1) + P(w2|w1)*P(w1)]
=
=
RELATED QUESTIONS
A urn contains n black balls and n white balls. Three balls are chosen from the urn at... (answered by math_helper)

Two balls are drawn (without replacement) from an urn that contains four balls, five... (answered by Nate)

Please help? Two urns contain each contain white balls and black balls. Urn 1 contains... (answered by fractalier,Fermat,AnlytcPhil)

An urn contains six red balls, five white balls, and four black balls. Four balls are... (answered by Fombitz)

An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2... (answered by ikleyn)

An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2... (answered by ikleyn,math_tutor2020)

An urn contains 5 balls. Two balls are drawn and are found to be What is the probability... (answered by stanbon)

An urn contains 40 balls. Some are red balls and the rest are white balls. If the... (answered by Shin123)

An urn contains 5 white and 7 black balls. Another urn contains 3 white and 9 black... (answered by greenestamps)