Some numbers about finding a dual

[BrainlessSquid]

If I did some calculation wrong, please tell me. But this is what I have found:

Lets say your dual represents 1/250 of the population. Then the likelihood of you finding a dual in a random meeting with a single person is 0.05. If you want to find one with at least 99% likelihood then:

the probability of not finding a dual in a single meeting = 0.995

now the probability of (not finding a dual after n meetings) = (0.995)^n, n = 0, 1, 2, ...

We want the probability of finding one to be at least 99%, then 1 - (0.995)^n > 0.99

Then n > log(0.01)[base 0.995] = 919.

This means you need to talk to 919 people to have at least 99% of likelihood of finding an ordinary dual. Which is more realistic than expecting to talk to 250 people to find one.

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Now, Lets say your dual represents 1/16 of the population.

then n > log(0.01)[base 15/16] = 73. Which means you only need to talk to 73 people to have at least 99% of likelihood of meeting an ordinary dual. Which is more realistic than talking to 16 people and hoping to find one.

It means that if your dual is more likely to be found than average, you need to talk to less than 73 people to have at least 99% of likelihood of meeting him/her.


Notes:

-these numbers work like a worst case scenario, because you could, for example, have the luck of finding 2, 3, 4 duals among those people. But you are 99% sure of finding at least one.
-for a type of 10%, you would still need to meet 44 people, because you kinda want to make SURE (or be 99% sure) of finding at least one.
-finding a dual is not the same as noticing them. so I'd suggest changing "meeting" to "getting to know" for better results
-noticing them is not the same as liking them. in this case, there's not much math can do about it, at this level of simplicity at least.