Question

掷两个骰子。两个点数的乘积是 $5$ 的倍数的概率是多少？

Two dice are thrown. What is the probability that the product of the two numbers is a multiple of $5?$

$\dfrac{1}{36}$

$\dfrac{1}{18}$

$\dfrac{1}{6}$

$\dfrac{11}{36}$

$\dfrac{1}{3}$

乘积是 $5$ 的倍数的唯一方法是至少一个骰子掷出 $5$ 。

用补集计数。两个骰子都不掷出 $5$ 的概率是 $\dfrac{5}{6} \cdot \dfrac{5}{6} = \dfrac{25}{36}.$

因此至少一个骰子掷出 $5$ 的概率为 $1 - \dfrac{25}{36} = \dfrac{11}{36}.$

所以正确答案是 D。

The only way for the product to be a multiple of $5$ is if at least one of the rolls is $5.$

We can do complementary counting. The probability that neither rolls is a $5$ is $\dfrac{5}{6} \cdot \dfrac{5}{6} = \dfrac{25}{36}.$

Therefore, the probability that at least one roll is a $5$ is $1 - \dfrac{25}{36} = \dfrac{11}{36}.$

Thus, D is the correct answer.