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锦程Connie · 2022年05月03日

请问计算器怎么按?

NO.PZ2016062402000015

问题如下:

On a multiple-choice exam with four choices for each of six questions, what is the probability that a student gets fewer than two questions correct simply by guessing?

选项:

A.

0.46%

B.

23.73%

C.

35.60%

D.

53.39%

解释:

We use the density given by Equation: f(x)=(nx)px(1p)nxf{(x)}={(\begin{array}{l}n\\x\end{array})}p^x{(1-p)}^{n-x}. The number of trials is n = 6. The probability of guessing correctly just by chance is p = 1/4 = 0.25. The probability of zero lucky guesses is C600.2500.756=0.756=0.17798C_6^00.25^00.75^6=0.75^6=0.17798. The probability of one lucky guess is C610.2510.755=6×0.25×0.755=0.35596C_6^10.25^10.75^5=6\times0.25\times0.75^5=0.35596. The sum is 0.5339.

Note that the same analysis can be applied to the distribution of scores on an FRM examination with 100 questions. It would be virtually impossible to have a score of zero, assuming random guesses; this probability is 0.75100=3.2E130.75^{100}=3.2E-13. Also, the expected percentage score under random guesses is p = 25%.

老师好,请问这题中的二项式计算(下面)用计算器怎么按?谢谢!

C60 *0.250*0.756




1 个答案

李坏_品职助教 · 2022年05月03日

嗨,努力学习的PZer你好:


C6,0就是从6个样本里随机抽取0个的组合数,意思就是一个都不选,也就是说所有6道题目全部做错了,那么概率就是0.25^0 * 0.75^6.


按下:0.75,y^x(有这个按键,在乘号×左侧),6,×,0.25

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