AMC10 2006 B

AMC10 2006 B · Q17

AMC10 2006 B · Q17. It mainly tests Probability (basic).

Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process the contents of the two bags are the same?

Bob 和 Alice 各有一个袋子，里面各有一个蓝、绿、橙、红、紫色的球。Alice 随机从她的袋子里选一个球放入 Bob 的袋子。然后 Bob 随机从他的袋子里选一个球放入 Alice 的袋子。经过这个过程后，两个袋子的内容相同概率是多少？

(A) 1/10 1/10

(B) 1/6 1/6

(D) 1/3 1/3

(E) 1/2 1/2

Answer

Correct choice: (D)

正确答案：（D）

Solution

After Alice puts the ball into Bob's bag, his bag will contain six balls: two of one color and one of each of the other colors. After Bob selects a ball and places it into Alice's bag, the two bags will have the same contents if and only if Bob picked one of the two balls in his bag that are the same color. Because there are six balls in the bag when Bob makes his selection, the probability of selecting one of the same colored pair is $\frac{2}{6} = \frac{1}{3}$.

Alice 把球放入 Bob 的袋子后，他的袋子有六个球：一种颜色有两个，其他颜色各一个。Bob 选球放入 Alice 的袋子后，两个袋子内容相同当且仅当 Bob 选到他袋子里那两个相同颜色的球之一。因为有六个球，选到相同颜色对的概率是 $\frac{2}{6} = \frac{1}{3}$。

Topics

CP.006 Probability (basic)