CE maths problem
2006-12-11 10:08 pm
Alfred's class has 41 students.One day,Alfred secretly tells one classmate a rumour.This classmate in turn chooses another classmate at random to spread the rumour to him.If the class spreads the rumour around in this manner,find the probability that the rumour still has not returned to Alfred after it is told 10 times(including the time Alfred told the rumour)
回答 (3)
2006-12-11 10:16 pm
✔ 最佳答案
1st time Alfred told the rumour to A
2nd time
A told the rumour to B
the chance that B is not Alfred is 1/40 ( 40 people and A )
3rd time
B told the rumour to C
the chance that C is not Alfred is 1/40
the chance that rumour does not return in this stage = the chance that both B and C is not Alfred = 1/40 * 1/ 40 = 1/1600
Similarly, 4th time, 5th time, 6th time, 7th time, 8th time, 9th time, 10th time
the person must not be Aflred
Therefore, answer =
1/40 * 1/40 * 1/40 * 1/40 * 1/40 * 1/40 * 1/40 * 1/40 * 1/40 = (1/40)^9
參考: me
2006-12-15 11:05 pm
41students
2006-12-12 6:41 am
There are 41 students.
1st turn, Alfred told the rumour to A.
2nd turn, A told the rumour to another classmate, B,
who can be anyone, but not Alfred.
3rd turn, when B spread the rumour to another classmate, not A.
It left 39 classmates to choose randomly (41 minus A & B),
so the chance that not return to Alfred is 38/39.
Similarly, for the 4th to 10th turn,
the chance for each turn that not return to Alfred is also 38/39.
Therefore, the probability is (38/39)^8
2006-12-22 12:22:59 補充：
pls be careful. the answer is incorrect!
1st turn, Alfred told the rumour to A.
2nd turn, A told the rumour to another classmate, B,
who can be anyone, but not Alfred.
3rd turn, when B spread the rumour to another classmate, not A.
It left 39 classmates to choose randomly (41 minus A & B),
so the chance that not return to Alfred is 38/39.
Similarly, for the 4th to 10th turn,
the chance for each turn that not return to Alfred is also 38/39.
Therefore, the probability is (38/39)^8
2006-12-22 12:22:59 補充：
pls be careful. the answer is incorrect!
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https://hk.answers.yahoo.com/question/index?qid=20061211000051KK01475