AMC8 2014

AMC8 2014 · Q12

AMC8 2014 · Q12. It mainly tests Permutations, Probability (basic).

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?

一本杂志刊登了三位名人的照片以及三张这些名人婴儿时期的照片。婴儿照片没有标明名人身份。读者被要求将每位名人与正确的婴儿照片对应起来。随机猜测的读者全部匹配正确的概率是多少？

(A) \frac{1}{9} \frac{1}{9}

(B) \frac{1}{6} \frac{1}{6}

(D) \frac{1}{3} \frac{1}{3}

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

Solution

For the first celebrity, you have a 1/3 chance of picking the photo. Given you get the picture right, you now have a 1/2 chance of picking the next photo. If you get both of them right, you are guarenteed to get the third right. Thus the probability is 1/2*1/3 which is 1/6.

对于第一位名人，选对照片的概率是 \( \frac{1}{3} \)。在选对第一张照片的前提下，选对第二张照片的概率是 \( \frac{1}{2} \)。如果前两张都选对了，第三张照片就必然正确。因此，概率是 \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \)。

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