I love probability

Q:  What is the probability that a positive integer no larger than 100 selected at random (among these integers) is divisible by 3?

A:  Well, there are 100 total positive integers that are “no larger than 100.”  Right?  This is all of the numbers 1-100.

Now we need to know how many numbers from 1-100 are divisible by 3… These are: 3, 6, 9, 12, 15, …. We don’t want to count them all!  So, 100 / 3 = 33.33333  Round down to 33.  There are 33 numbers from 1-100 that are divisible by 3.

So, if we select a number randomly from 1-100, we have a 33/100 chance to pick a number that is divisible by 3.

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