AMC10 2005 A

AMC10 2005 A · Q9

AMC10 2005 A · Q9. It mainly tests Probability (basic).

Three tiles are marked X and two other tiles are marked O. The five tiles are randomly arranged in a row. What is the probability that the arrangement reads XOXOX?

有 3 块标有 X 的瓦片和 2 块标有 O 的瓦片。5 块瓦片随机排成一排。排列为 XOXOX 的概率是多少？

(A) $\frac{1}{12}$ $\frac{1}{12}$

(B) $\frac{1}{10}$ $\frac{1}{10}$

(D) $\frac{1}{4}$ $\frac{1}{4}$

(E) $\frac{1}{3}$ $\frac{1}{3}$

Answer

Correct choice: (B)

正确答案：（B）

Solution

There are three X's and two O's, and the tiles are selected without replacement, so the probability is $\frac{3}{5} \cdot \frac{2}{4} \cdot \frac{2}{3} \cdot \frac{1}{2} \cdot \frac{1}{1} = \frac{1}{10}$.

有三个 X 和两个 O，瓦片无放回选择，所以概率是 $\frac{3}{5} \cdot \frac{2}{4} \cdot \frac{2}{3} \cdot \frac{1}{2} \cdot \frac{1}{1} = \frac{1}{10}$。

Topics

CP.006 Probability (basic)