AMC8 2019

AMC8 2019 · Q18

AMC8 2019 · Q18. It mainly tests Probability (basic), Parity (odd/even).

The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number?

两个公平骰子的每个面都编号为 1、2、3、5、7 和 8。抛掷这两个骰子时，它们的和为偶数的概率是多少？

(A) \frac{4}{9} \frac{4}{9}

(B) \frac{1}{2} \frac{1}{2}

(D) \frac{3}{5} \frac{3}{5}

(E) \frac{2}{3} \frac{2}{3}

Answer

Correct choice: (C)

正确答案：（C）

Solution

We have $2$ dice with $2$ evens and $4$ odds on each die. For the sum to be even, the 2 rolls must be $2$ odds or $2$ evens. Ways to roll $2$ odds (Case $1$): The total number of ways to obtain $2$ odds on 2 rolls is $4*4=16$, as there are $4$ possible odds on the first roll and $4$ possible odds on the second roll. Ways to roll $2$ evens (Case $2$): Similarly, we have $2*2=4$ ways to obtain 2 evens. Probability is $\frac{20}{36}=\frac{5}{9}$, or $\framebox{C}$.

每个骰子有 2 个偶数和 4 个奇数。要使和为偶数，必须两个都是奇数或两个都是偶数。情况 1：两个奇数的方式：4*4=16 种。情况 2：两个偶数的方式：2*2=4 种。概率是 \frac{20}{36}=\frac{5}{9}，即 \framebox{C}。

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