» Title: 補救教學(9)—使機率高達0.999» Posted: 6月 4th, 2013» Author: 我是大富翁» Filed Under: 數學.
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補救教學(9)—使機率高達0.999
一校隊王顥投籃,他的實力統計是平均每5球命中4球, 問他應該要連投幾球,才會使至少命中一發的機率大於0.999?
(詳解): 王顥的每一次投球的命中率=0.8,不命中的機率=0.2 假設教練小蔡老師要求他至少命中一發的水準必須>0.999 (不必百分之百,也不可能百分之百,永遠不會miss),
設他連投n球,至少命中一發的機率為p,題意即要求出n,使
p>0.999 此即-p<-0.999, 兩邊同加1, 則1-p<0.001, 而1-p正是p的否定,也就是說,1-p是他連投n發,而這n發通通摃龜之機率,
所以有
答案:他至少須要連發5發才辦得到。
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