A bag contains two white balls and two black balls.You draw two balls out.What is the propability of the two balls that you draw are the same colour?
Answer 1: You list all the cases:WW,WB,BW,BB. In the four cases,WW and BB is match the question.So the propability of the two balls that you draw are the same colour is 2/4=1/2
Answer 2: First, you draw a ball. Its colour may be black,or white. If it's black,then the bag is left with B,W,W. There is only one B left.And if it's white,then there is only one W left.So the propability of the two balls that you draw are the same colour is [(1/2)x(1/3)]+[(1/2)x(1/3)]=1/3
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propability
2009-10-10 6:03 am
回答 (2)
2009-10-10 6:43 am
✔ 最佳答案
The first answer is wrong. Although there are four different combinations, the probability of occurrence for each of the combinations are not the same. Consider drawing 2 balls from a total of 4, there are C(4,2) combinations, i.e. 6 ways.
If we labelled the balls as W1, W2, B1, B2, it will become more obvious. The 6 combinations are: W1W2, W1B1, W1B2, W2,B1, W2,B2 and B1,B2. Therefore the probability of drawing 2 balls of the same colour is 2/6 = 1/3.
2009-10-12 4:27 am
agree with nelsonywm2000
for 1st answer, you should differentiate
w1 and w2
i.e. there are four balls: W1,W2,B1,B2
so there are 6 ways
2009-10-11 20:29:36 補充：
for the 2nd one, it can be simplified as
no matter which ball you choose at the beginning
there must be one and only one ball out of three which you want to get
i.e. one desired ball out of three balls that is going to be the second one drawn
for 1st answer, you should differentiate
w1 and w2
i.e. there are four balls: W1,W2,B1,B2
so there are 6 ways
2009-10-11 20:29:36 補充：
for the 2nd one, it can be simplified as
no matter which ball you choose at the beginning
there must be one and only one ball out of three which you want to get
i.e. one desired ball out of three balls that is going to be the second one drawn
收錄日期: 2021-04-23 23:17:59
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