# Probability of one number from infinite [duplicate]

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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?

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

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## 1 Answer

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.