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jmc

counting and probability intermediate

Problem

An integer greater than 9 and less than 100 is randomly chosen. What is the probability that its digits are different?
Solution
We calculate the probability that the digits are the same, and subtract from 1. From the 90 integers to be chosen from, only 9 have the same digits: 11, 22, 33, ..., 99. Therefore, the probability that the digits are the same is , so the probability that the digits are different is .
Final answer
\frac{9}{10}