If you randomly take a positive integer and divide it by 23, what’s the probability that the remainder is 13?

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- Jul 8th 2010, 11:19 PMlifeunderwaterProbability Question involving remainders
If you randomly take a positive integer and divide it by 23, what’s the probability that the remainder is 13?

- Jul 8th 2010, 11:23 PMAlso sprach Zarathustra
Hint:

For any random number divided by 23 has finite number of remainders.

The group of remainders modulus 23:

{0,1,2,3,4,5,6,7,...,19,20,21,22} - Jul 8th 2010, 11:28 PMlifeunderwater
Sorry, But I don't understand the question or the hint you gave me :(

- Jul 9th 2010, 05:03 AMmr fantastic
Since the sample space is infinite, answering this question in a rigorous way is less trivial than meets the eye.

However, it's probably meant to be answered in a trivial way, in which case you have already been given a good hint.

Out of every 23 consecutive positive integers, one of them is evenly divisible by 23, one produces a remainder of 1, one produces a remainder of 2, . . . . . , one produces a remainder of 22. So you could argue that the probability that a random integer will produce a remainder of 13 is ...... (where ...... means insert your answer here).