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This question already has an answer here:

If we find probability of getting a number, say 800, from the set of infinite then the probability would be 1/infinite which is 0, but there are some possibilities to get 800. How!? Where am I wrong?

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marked as duplicate by Adrian Keister, user296602, Jaap Scherphuis, Community Jan 14 at 16:38

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I think you have two mis-conceptions. First, you're assuming that probability zero can't happen. That's what we tell beginners, but actually, probability zero CAN happen. E.g., let your height be $h$ inches, where $h$ is a real number. There are infinite possibilities for $h$, but yet it settled on one. The probability that you are the height that you are was zero, but it happened.

Second, you're assuming a uniform distribution, that is, you assume all numbers are equally likely to be chosen. That's probably not the case. If you ask a million people to chose a positive integer, a number like $800$ is apt to come up at least one. But a number like $12,345,543,5432,323,234,762,345$ has a very small probability of being chosen. So with a more realistic distribution function, you might have the probability of $800$ be non-zero.

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