0.1變成0.65這是什麼狀況

蘋果花的老公
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2017/11/21
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2 mins read


昨天數學老師又出了一些奇怪的題目

題目內容如下

有一神射手,其槍法十分準確。

對於在五十公尺遠的目標,有90%的機率可射擊命中。

今對於此目標連續射發十次,並假設十次擊發彼此皆為獨立事件。

試問此神射手至少失誤一發的機率。

原本想說這個題目應該沒什麼困難

因為他每次都有90%的命中率

那他這10次不就有一次不會中嗎

但是他後面加了一個獨立事件

為什麼是獨立事件呢

經過了一個晚上的反覆思考

我終於想通了一件事

他每次射出一支弓箭只有90%的命中率

然而他做了10次同樣的行為

所以是0.9的10次方

得出來的結果是0.3486784401

但是這個結果並不是正確的

因為他後面又加了一個至少失誤1發的機率

因此我又想到了另外一個他叫做餘集法則

所以正確的運算式變成了1減0.9的10次方

理所當然那正確的解答就變成0.6513215599

如果沒有看清楚題目就寫答案的話

結果就會差6.5倍


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