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개념 기사 기사 작성법
내가 아는 수학개념을 쉽게 설명해주세요!
[개념 기사] 행운의 확률은 63%
GUN.007 2020.05.10 04:30
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

흔히 사람들은 "인생은 50대 50"이라고들 말합니다.

'좋은 일 반, 나쁜 일 반' 이라는 뜻이죠.

근데 이 한 문제를 보면 꼭 50대 50인 것은 아니라는 것을 느낄 것입니다.

이 문제는 피에르 몽모르의 '만남의 문제'라 불립니다.

https://www.google.com/search?q=%ED%96%89%EC%9A%B4&tbm=isch&ved=2ahUKEwiqybrkyKbpAhUoHKYKHS45BUoQ2-cCegQIABAA&oq=%ED%96%89%EC%9A%B4&gs_lcp=CgNpbWcQAzICCAAyAggAMgIIADICCAAyAggAMgIIADICCAAyAggAMgIIADICCAA6BggAEAgQHjoECAAQGFDjNFjwQ2DFRWgAcAB4A4ABd4gB6AiSAQM0LjeYAQCgAQGqAQtnd3Mtd2l6LWltZ7ABAA&sclient=img&ei=XoW2XqqiJKi4mAWu8pTQBA&bih=875&biw=1280&rlz=1C1ASAC_enKR474KR496#imgrc=k8XaryIBBv5slM

'만남의 문제'문제

 

A와 B라는 사람이 트럼프를 에이스부터 킹까지 13장씩 가지고 책상 위에 

한 장씩 내놓으면서 '짝 맞추기'를 합니다.

같은 숫자의 카드가 동시에 나오면 '만남', 그렇지 않으면 '만남'이 아닙니다.

그럼 13장을 모두 내놓았을 때 '만남'이 하나도 없을 확률은 얼마일까? 

그리고 카드의 장수를 n장이라고 했을 때의 확률은?

https://www.google.com/search?q=%ED%8A%B8%EB%9F%BC%ED%94%84+%EA%B2%8C%EC%9E%84&rlz=1C1ASAC_enKR474KR496&source=lnms&tbm=isch&sa=X&sqi=2&ved=2ahUKEwjhnZPjyKbpAhXWvp4KHYhpAH4Q_AUoAXoECBMQAw&biw=1280&bih=875#imgrc=2_ASxeYyLq0AqM&imgdii=tDrF362Klv5LkM

 

이 문제가 나온 후 30여년 후 천재수학자 '레온하르트 오일러'가 이 문제를 풀었다 합니다.

그 결과 'n'의 값과 거의 상관없이 확률은 보통 약 37%가 나왔다고 합니다.

이것은 1A에 1B이외의 카드가 대응하고 2A에는 2B이외의 카드가 대응하는 식으로 불일치하는

모든 순열의 수를 구하면 알 수 있습니다.

 

카드가 3장씩일 경우로 예를 들면(쉬워서 예로 듭니다)

A의 경우, A의 (1,2,3)에 대해 B는 (2,3,1),(3,1,2)여야 합니다.

이때의 확률은 약 33%가 됩니다.(정확히는 1/3)

일치하는 결과지요.

 

생활 속으로 한번 들어가 보죠.

선을 볼 때 여러 기준을 정할 것입니다. '외모', '소득' 등과 같은 것 말이죠.

하지만 모든 기준을 만족하는 사람은 찾기 힘들 것입니다. 그래서 계속 보다보면

기준이 내려가 한게까지고 내려갈 수 있죠.

이때 보면 10명중 한 6명은 괜찮을 것이죠.

 

어떤가요?

좀 더 긍정적으로 살아보는 건 어떨까요?

 

<오늘의 퀴즈>

만남의 문제를 제기한 사람은?

1. 피에르 페르마

2. 피카츄 라이츄

2. 피에르 몽모르

태그
#만남의문제 #몽모르 #오일러 #행운은 #63% #매스포터데이 #확률

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