Question

罐子里有编号 $1$ 到 $10$ 的十个球。Jack 伸手随机取出一个球。然后 Jill 伸手随机取出另一个不同的球。取出的两个球上的数字之和为偶数的概率是多少？

Ten balls numbered $1$ to $10$ are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. What is the probability that the sum of the two numbers on the balls removed is even?

$\dfrac{4}{9}$

$\dfrac{9}{19}$

$\dfrac{1}{2}$

$\dfrac{10}{19}$

$\dfrac{5}{9}$

答案：A

知识点：基本概率奇偶性

难度评级：1090

解答：

和为偶数时，两个球同为奇数或同为偶数。全奇的配对有 $\binom{5}{2} = 10$ 对，全偶的配对也有 $\binom{5}{2} = 10$ 对，共 $20$ 对有利情况。

总配对数是 $\binom{10}{2} = 45$ ，所以概率是 $\dfrac{20}{45} = \dfrac49$ 。

所以正确答案是 A。

The sum is even when both balls are odd or both are even. There are $\binom{5}{2} = 10$ all-odd pairs and $\binom{5}{2} = 10$ all-even pairs, for $20$ favorable pairs.

The total number of pairs is $\binom{10}{2} = 45,$ so the probability is $\dfrac{20}{45} = \dfrac49.$

Thus, the correct answer is A .

1987 AMC 8 第 25 题

答案：A

难度评级：1090

解答：

其他年份的第 25 题