题目

What is the probability P that A and B are both selected when you select 40 people out of a group of 100 (A and B included)?


Quantity A

p

Quantity B

选项

A.

Quantity A is greater.


B.

Quantity B is greater.


C.

The two quantities are equal.


D.

The relationship cannot be determined from the information given.


解析

我们已经选定A和B两人,因此需要从剩余的$100-2=98$人中再选出38人。 选法数为$\binom{98}{38}$ 总选法数为$\binom{100}{40}$ 概率: p = \frac{\binom{98}{38}}{\binom{100}{40}} p = \frac{98!}{38! \cdot 60!} \times \frac{40! \cdot 60!}{100!} p = \frac{98! \cdot 40!}{38! \cdot 100!} = \frac{40 \times 39}{100 \times 99} = \frac{26}{165} 因此,答案为选项C
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