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Fran randomly chooses a positive integers n, 1 <= n <= 100. Find the probability that \(n/21\) is reducible.

 May 15, 2022
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If n/21 is reducible, then either n is a multiple of 3 or n is a multiple of 7.

 

There are floor(100/3) = 33 multiples of 3 from 1 to 100, and there are floor(100/7) = 14 multiples of 7 from 1 to 100.

But we have double counted floor(100/21) = 4 multiples of 21, so the total number of integers n with 1 <= n <= 100 such that n/21 is reducible is 33 + 14 - 4 = 43.

 May 16, 2022

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