AMC 8 2014 Problem 12
AMC8 2014 年第 12 题
概率★★★☆☆
A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly?
一家杂志社打印了 3 位名人的照片，以及这 3 位名人婴儿时的照片。从婴儿照片上无法识别出对应的名人。杂志社要求读者把每位名人的照片和对应的婴儿照片正确匹配。某个读者随机匹配了这些照片，那么他把这 3 个名人都正确匹配的概率是多少？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
For the first celebrity, you have a chance of picking the photo. Given you get the picture right, you now have a chance of picking the next photo. If you get both of them right, you are guaranteed to get the third right. Thus the probability is * which is . -JasonDaGoat
Let's call the celebrities A, B, and C. There is a chance that celebrity A's picture will be selected, and a chance that his baby picture will be selected. That means there are two celebrities left. There is now a chance that celebrity B's picture will be selected, and another chance that his baby picture will be selected. This leaves a chance for the last celebrity, so the total probability is . However, the order of the celebrities doesn't matter, so the final probability will be .
There is a chance that the reader will choose the correct baby picture for the first person. Next, the second person gives a chance, and the last person leaves only 1 choice. Thus, the probability is .
There are 3! ways assign the pictures to each of the celebrities. There is one favorable outcome where all of them are matched correctly, so the answer is .
继续练习