Two urns contain some coloured balls.
Urn A contains 12 balls: 8 are black, 4 are white.
Urn B contains 15 balls: 9 are black , 6 are white.
A ball is drawn at random from urn A to placed in urn B.
A ball is thendrawn at random from urn B, which now contains sixteen balls.
What is the probability that the ball drawn from urn B is black?
Ans : 29/48
Q: Given that the ball drawn from urn B was black, what is the probability that the ball drawn from urn A was also black?
Ans: 20/29
F.7 Probability [20points]
2011-09-29 7:20 pm
回答 (2)
2011-09-29 7:32 pm
✔ 最佳答案
1)P(The ball drawn from urn B is black)= P(A black ball is drawn from urn A to placed in urn B and then a black ball drawn from urn B)
+
P(A white ball is drawn from urn A to placed in urn B and then a black ball drawn from urn B)= (8/12)(10/16) + (4/12)(9/16)= 29/48
2)
P(The ball drawn from urn A was also black given that the ball drawn from urn B was black)= P(A black ball is drawn from urn A to placed in urn B and then a black ball drawn from urn B) / P(The ball drawn from urn B is black)= (8/12)(10/16) / (29/48)= 20/29
2011-09-29 7:34 pm
(a) P(the ball from urn B is black)
= P(the ball from urn B is black|the ball from urn A is black)P(the ball from urn A is black) + P(the ball from urn B is black|the ball from urn A is white)P(the ball from urn A is white)
= (10/16)(8/12) + (9/16)(4/12)
= 29/48
(b) (10/16)(8/12)/[(10/16)(8/12) + (9/16)(4/12)]
= 20/29
= P(the ball from urn B is black|the ball from urn A is black)P(the ball from urn A is black) + P(the ball from urn B is black|the ball from urn A is white)P(the ball from urn A is white)
= (10/16)(8/12) + (9/16)(4/12)
= 29/48
(b) (10/16)(8/12)/[(10/16)(8/12) + (9/16)(4/12)]
= 20/29
收錄日期: 2021-04-21 22:23:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110929000051KK00347