Probability 一問

👨🏻‍🏫 學術台數學

[匿名]

2007-09-03 3:07 pm

Suppose we randomly draw m people form the whole population. What is the probability that NO TWO PERSONS in this exmple have the same birthday?

答案是 if n=23, prpbability =0.4937, 有無人可以解釋一下啊﹖THANKS﹗﹗

更新1:

你好﹐好感謝你的回答﹐但係我有少少問題搞唔太清楚 (係我既問題) = 1(364/365)(363/365)(362/365)...(343/365) <--- 呢句我明點解﹐ = 365!/341!365^23 <-- 但係點解會引伸到呢句既﹖ 點解分子係 365!, 而分母係 341!365^23 ﹖

回答 (2)

heatthespurs

2007-09-04 12:17 am

✔ 最佳答案

I believe it should be 365!/342!365^23

Probability
= 1(364/365)(363/365)(362/365)...(343/365)
= (365/365)(364/365)(363/365)(362/365)...(343/365)
= (365 x 364 x 363 x … x 343) / 365^23

since 365 x 364 x 363 x … x 343 = 365! / 342!

so probability = 365!/342!365^23

--------

In general, if you can notice that 342 = 365 - 23

then the answer can be generalized to 365!/(365-n)!365^n

in this case, n=23

^_^

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Ada

2007-09-03 3:23 pm

這是假設一年有365天
我們每次抽一人
第一人抽誰也沒有問題
所以機會是1
第二個不可抽和第一人相同的生日的
所以機會是 364/365
第三個則是 363/365
如此類推
至第廿三項為 343/365
所以所求機率
= 1(364/365)(363/365)(362/365)...(343/365)
= 365!/341!365^23
= 0.49...

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