SOLUTION: Please help me on this question.
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. Blindfolded, y
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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. Blindfolded, y
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Question 1183551: Please help me on this question.
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. 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) (Show Source):
a) P(B) = P(B|(U1 and W))*P(W|U1)*P(U1) + P(B|(U1 and B))*P(B|U1)*P(U1) +
P(B|(U2 and W))*P(W|U2)*P(U2) + P(B|(U2 and B))*P(B|U2)*P(U2)
= 3/28 + 4/21 + 5/32 + 1/8 = , approximately 0.57887 to 5 d.p.
b) P(U2|B) = P(U2 and B)/P(B) = (9/32)/(389/672) = , approximately 0.48586 to 5 d.p.
