A box contains 10 balls of which 5 are red. Suppose we pick out balls randomly one
by one without replacement, until we get 3 red balls. What is the probability that we
have picked out 6 balls in total?
Probability Question
2015-04-24 4:30 am
回答 (2)
2015-04-24 5:30 am
✔ 最佳答案
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2015-04-24 7:38 am
There are 5 red balls and 5 non-red balls.
6 balls are picked out in total until we get 3 red balls. This means that 3 non-red ball and 2 red balls are firstly picked out, and then the 6th ball is red.
Pr(Firstly pick out 3 non-red balls and 2 red balls)
= 5C3 × 5C2 / 10C5
= 10 × 10 / 252
= 25/63
2015-04-23 23:38:40 補充：
Pr(the 6th ball is red after picking out 3 non-red balls and 2 red balls)
= (5 - 2) / (10 - 5)
= 3/5
The required probability
= (25/63) × (3/5)
= 5/21
6 balls are picked out in total until we get 3 red balls. This means that 3 non-red ball and 2 red balls are firstly picked out, and then the 6th ball is red.
Pr(Firstly pick out 3 non-red balls and 2 red balls)
= 5C3 × 5C2 / 10C5
= 10 × 10 / 252
= 25/63
2015-04-23 23:38:40 補充：
Pr(the 6th ball is red after picking out 3 non-red balls and 2 red balls)
= (5 - 2) / (10 - 5)
= 3/5
The required probability
= (25/63) × (3/5)
= 5/21
收錄日期: 2021-04-15 19:08:14
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150423000051KK00071