Asked by Annely
Urn A contains six white balls and three black balls. Urn B contains seven white balls and five black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was white given that the second ball drawn was white?
Answers
Answered by
Reiny
2 initial cases:
case 1, the ball drawn from urn A to B is W
urn B now has 8W and 5B
prob (W and W)
= prob(W from A AND W from B)
= <b>(6/9)(8/13) = 48/117</b>
rest of problem to check my answer:
prob(W and B) = (6/9)(5/13) = 30/117
case2: the ball from urn A to urn B is B
Prob(B and W)
= (3/9)(7/13) = 21/117
prob(B and B) = 18/117
sum of the 4 possibilities should be 1
48/117 = 30/117 + 21/117 + 18/117
= 117/117
= 1
looks good to me
case 1, the ball drawn from urn A to B is W
urn B now has 8W and 5B
prob (W and W)
= prob(W from A AND W from B)
= <b>(6/9)(8/13) = 48/117</b>
rest of problem to check my answer:
prob(W and B) = (6/9)(5/13) = 30/117
case2: the ball from urn A to urn B is B
Prob(B and W)
= (3/9)(7/13) = 21/117
prob(B and B) = 18/117
sum of the 4 possibilities should be 1
48/117 = 30/117 + 21/117 + 18/117
= 117/117
= 1
looks good to me
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.