ExplanationThe first 100 positive integers comprise the set of numbers containing the integers 1 to 100.

Of these numbers, the only ones that are divisible by 3 are {3, 6, 9, …, 96, 99}, which adds up to exactly 33 numbers. This can be determined in several ways. One option is to count the multiples of 3, but that’s a bit slow. Alternatively, compute \(\frac{99}{3}= 33\) and realize that there are 33 multiples of 3 up to and including 99.

The number 100 is not divisible by 3, so the correct answer is \(\frac{33}{100}\).

Alternatively, use the “add one before you’re done” trick, subtracting the first multiple of 3 from the last multiple of 3, dividing by 3 and then adding 1: \(\frac{99-3}{3}+ 1 = 33\).

Then, since probability is determined by the number of desired options divided by the total number of options, the probability that the number chosen is a multiple of 3 is \(\frac{33}{100}\).

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Sandy

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