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袁翀 · 2021年09月20日

这一题是否可以用如下思路

NO.PZ2018062016000082

问题如下:

The stock of AAA company has a 30% probability to rise every year, if every annual trial is independent from each other, the probability that the stock will rise more than 1 time in the next 3 years is:

选项:

A.

0.145

B.

0.216

C.

0.377

解释:

B is correct. Based on the corresponding formula:

p(x)=P(X=x)=(nx)px(1p)nxp{(x)}=P{(X=x)}={(\begin{array}{c}n\\x\end{array})}p^x{(1-p)}^{n-x}, n = 3 and p = 0.30.

p(2)=3!(32)!2!×0.32(10.3)1=(3)(0.09)(0.7)=0.189p(2)=\frac{3!}{(3-2)!2!}\times0.3^2(1-0.3)^1=\left(3\right)\left(0.09\right)\left(0.7\right)=0.189.

p(3)=3!(33)!3!×0.33(10.3)0=(1)(0.027)(1)=0.027p(3)=\frac{3!}{(3-3)!3!}\times0.3^3(1-0.3)^0=\left(1\right)\left(0.027\right)\left(1\right)=0.027\cdot

The required probability is: p(2) + p(3) = 0.189 + 0.027 = 0.216

求解未来三年至少还有一年上涨的概率是否可以想成排出三年来一次都不上涨的概率,即1-0.7*0.7*0.7。但是这种思路算出来的结果与标准答案大相径庭,错误之处在哪里呢?
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已采纳答案

星星_品职助教 · 2021年09月20日

同学你好,

这个思路方向可以,但少考虑了一种情况。

“the probability that the stock will rise more than 1 time in the next 3 years”的反面是三年一次都没上涨,和三年只上涨一次

即,P(X≤1)有P(X=0)和P(X=1)两种情况:

P(0)=0.7×0.7×0.7=0.343 三年都没有rise,这是你考虑到的情况。

P(1)=3C2×30%×70%×70%=0.441

最后 1-P(X≤1)=1-0.343-0.441=0.216

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NO.PZ2018062016000082 问题如下 The stoof Acompany ha 30% probability to rise every year, if every annutriis inpennt from eaother, the probability ththe stowill rise more th1 time in the next 3 years is: A.0.145 B.0.216 C.0.377 B is correct. Baseon the corresponng formula:p(x)=P(X=x)=(nx)px(1−p)n−xp{(x)}=P{(X=x)}={(\begin{array}{c}n\\x\enarray})}p^x{(1-p)}^{n-x}p(x)=P(X=x)=(nx​)px(1−p)n−x, n = 3 anp = 0.30.p(2)=3!(3−2)!2!×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189p(2)=\frac{3!}{(3-2)!2!}\times0.3^2(1-0.3)^1=\left(3\right)\left(0.09\right)\left(0.7\right)=0.189p(2)=(3−2)!2!3!​×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189.p(3)=3!(3−3)!3!×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅p(3)=\frac{3!}{(3-3)!3!}\times0.3^3(1-0.3)^0=\left(1\right)\left(0.027\right)\left(1\right)=0.027\ctp(3)=(3−3)!3!3!​×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅The requireprobability is: p(2) + p(3) = 0.189 + 0.027 = 0.216 我算的是接下来3年均大于, 也就是p1+p2+p3均大于的情况, 请问这样理解为什么不对

2023-11-05 19:38 2 · 回答

NO.PZ2018062016000082 问题如下 The stoof Acompany ha 30% probability to rise every year, if every annutriis inpennt from eaother, the probability ththe stowill rise more th1 time in the next 3 years is: A.0.145 B.0.216 C.0.377 B is correct. Baseon the corresponng formula:p(x)=P(X=x)=(nx)px(1−p)n−xp{(x)}=P{(X=x)}={(\begin{array}{c}n\\x\enarray})}p^x{(1-p)}^{n-x}p(x)=P(X=x)=(nx​)px(1−p)n−x, n = 3 anp = 0.30.p(2)=3!(3−2)!2!×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189p(2)=\frac{3!}{(3-2)!2!}\times0.3^2(1-0.3)^1=\left(3\right)\left(0.09\right)\left(0.7\right)=0.189p(2)=(3−2)!2!3!​×0.32(1−0.3)1=(3)(0.09)(0.7)=0.189.p(3)=3!(3−3)!3!×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅p(3)=\frac{3!}{(3-3)!3!}\times0.3^3(1-0.3)^0=\left(1\right)\left(0.027\right)\left(1\right)=0.027\ctp(3)=(3−3)!3!3!​×0.33(1−0.3)0=(1)(0.027)(1)=0.027⋅The requireprobability is: p(2) + p(3) = 0.189 + 0.027 = 0.216 谢谢解答

2022-11-04 18:24 1 · 回答

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2022-08-21 16:46 1 · 回答

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2020-07-28 13:18 1 · 回答