Question

从集合 $\{1, 2, 3, \ldots, 100\}$ 中随机选一个整数，它能被 $2$ 整除但不能被 $3$ 整除的概率是多少？

What is the probability that an integer in the set $\{1, 2, 3, \ldots, 100\}$ is divisible by $2$ and not divisible by $3?$

$\dfrac{1}{6}$

$\dfrac{33}{100}$

$\dfrac{17}{50}$

$\dfrac{1}{2}$

$\dfrac{18}{25}$

先数 $2$ 的倍数，再去掉同时能被 $3$ 整除的数。

Count the multiples of $2,$ then remove those also divisible by $3$

有 $50$ 个偶数和 $16$ 个 $6$ 的倍数。

There are $50$ even numbers and $16$ multiples of $6$

$100$ 个整数中有 $50$ 个能被 $2$ 整除。

其中同时能被 $3$ 整除的是 $6$ 的倍数，共 $16$ 个。

因此符合条件的数有 $50 - 16 = 34$ 个，概率为 $\dfrac{34}{100} = \dfrac{17}{50}$ 。

所以正确答案是 C。

Of the $100$ integers, $50$ are divisible by $2.$

Among those, the ones also divisible by $3$ are the multiples of $6,$ of which there are $16.$

So $50 - 16 = 34$ qualify, giving probability $\dfrac{34}{100} = \dfrac{17}{50}.$

Thus, the correct answer is C.