Thales may not get rich as a gambler but Galaxiom won't win any prizes at maths until he learns about the Birthday Problem.
An elementary mistake. Of course I have calculated the probabliity of a particular number emerging rather than the repeat. Long ago I was actually quite good at maths but I have not studied statistics since 1978.
The specific instance now - what kind of BS statement is: "the probability of a duplicate is greater than 50:50 after fewer than 1E20 guids." "Fewer" meaning 1? Or two ? or 5? or 1E19?
Now if I rememebr correctly after 35 years....
The probability of a repeated number on a particular instance is the number of potential duplicates (one less than the number of draws.) divided by the total number of possible outcomes.
Where t as the total number of possible outcomes and n is the number of draws.
(n-1)/t
The chance of getting a duplicate within n instances is calculated by finding the chance of not getting any duplicates.
The chance of not getting a duplicate on the nth instance is:
1 - (n-1)/t
The chance of not getting a duplicate on any instance up to n is the product of the probabilities of all instances to that point.
(1 - 1/t) * (1 - 2/t) * ...... * (1 - (n-1)/t)
Or is it this?:
((1 - 1/t) + (1 - 2/t) + ...... *+ (1 - (n-1)/t))/n
Edir: Perhaps someone with better maths than me could answer this last bit correctly.
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