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pengyaning · 2023年10月14日

为什么不用二项分布？求解析！

  1. FRM I
  2. Quantitative

NO.PZ2023091601000029

问题如下：

A multiple choice exam has ten questions, with five choices per question. If you need at least three correct answers to pass the exam, what is the probability that you will pass simply by guessing?

选项：

A.0.8% B.

20.1%

C.

67.8%

D.

32.2%

解释：

The probability of an event is between 0 and 1. If these are mutually exclusive events, the probability of individual occurrences are summed. This probability follows a binomial distribution with a p-parameter of 0.2. The probability of getting at least three questions correct is 1 – [p(0) + p (1) + p (2)] = 32.2%.

为什么不用二项分布？求解析！

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1 个答案

李坏_品职助教 · 2023年10月14日

嗨，从没放弃的小努力你好：


这个就是用的二项分布（binomial distribution）


题目说至少需要答对3个题目才行，至少答对3个题目的概率= 1-P(0)-P(1)- P(2)，这P括号里的数字就是答对题目的个数。至少答对3个的概率=1减去答对0个、1个和2个题目的概率。


每一道题有5个选项，所以单独来看一道题答对的概率是0.2，答错的概率是0.8。

P(0) = 0.8^10 =0.107

P(1) = C(1,10) * 0.8^9 * 0.2 = 0.268

P（2）=C(2,10) * 0.8^8 * 0.2^2 = 0.302，

所以1-P(0)-P(1)-P(2) = 0.323

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