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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
sicma
2020.07.24 03:34
조회 571
중간고사를 보고나서 든 생각입니다.
sicma가 받은 중간고사는 총 25문제가 있었습니다.
배점은 다 똑같았고 5지선다 였다.
그렇다면 5개 중 하나를 찍어 맞출 확률은 1/5이다.
그런데 고등학교에서 8,9등급을 보면 0점이나 4점 8점은 별로 나오지 않고 20점 안팎이다. 그렇다면 이걸 보고 할 수 있는 추측이 들었다.
그렇다면 오지선다에서 아무렇게나 찍으면 맞을 확률인 1/5를 100에 곱한 20점 정도가 나온다. 가 맞는 것일까? 아니면 한 문제를 맞출 확률이 1/5니깐 20점을 맞을 확률은 극히 드물다.가 맞을까?
둘 중 어느 것이 맞을까?
(음.. 5개중 하나가 답이어서 1/5인건 알겠는데 아무것도 모르는 시험지를 보면 왜 20점이 잘 나올까라는 질문입니다.)
(단, 시험 문제는 풀지 않고 찍기만 한다.)
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Mata
Lv.6
2020.07.24 11:41
기댓값은 (확률)*(배당된 점수)의 총합이니까 이렇게 계산하면 이론상으로는 (0.2)*(배당된 점수들의 총합)=0.2*100=20이 되는 것 같습니다.
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sicma
Lv.11
2020.07.24 20:34
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△π
Lv.9
2020.08.03 04:31
전체 경우의 수를 따져서 이항정리로 풀면, (1/5^n)(4/5^25-n)x25Cn이 n=5일 때 정점을 찍기 때문에 그렇다고 생각합니다!
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sicma
Lv.11
2021.05.07 10:27
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