注目の話題: どうしても結婚したいです。; 昭和生まれ、集まれー！死語、何が浮かぶ？; 友人に裏切られ、どう対応して良いのか分かりません。

Science,English,and math Ⅱ

No.143　18/02/12 10:38
燻し銀三 ( 50代 ♂ Oe38xe ) あ+あ-

【An untrustworthy intuition.】

《There is a class composed of 40 students. The probability that a student’s birthday is same with other one is no less than 89%.》

The question is whether or not at least the birthday of the two students are same,we should think over the complementary event 余事象,first of all. The complementary event,in short,in this situation,it means all the students’ birthday is different. Then I'm going to get rid of 29th February in order to make the things simple.

I'm going to think over from the case of less students in turn. As for the two students, if a student’s birthday is fixed, the birthday of the other is among the other rest days in a year,so the probability that the two students’ birthday is different is 364-365ths.

What about if there are 3 students? If the two students’ birthday is different from the third one,the rest days are 363. As a result,the probability that the birthday of the first of two students are different from the third one is 363-365ths.