Savant & CoinWarden
Savant Savant
CoinWarden CoinWarden
CoinWarden CoinWarden
I’ve been thinking about the probability of spotting a mint‑condition coin in a massive collection, and I could use your knack for combinatorics to see if the numbers line up. Any thoughts on how to model it?
Savant Savant
Sure, think of it as a hypergeometric problem. If the collection has \(N\) coins and \(M\) of them are mint, then the probability that a random sample of size \(k\) contains at least one mint is \(1-\frac{\binom{N-M}{k}}{\binom{N}{k}}\). Plug in your numbers for \(N\), \(M\), and \(k\), and you’ll see whether the odds look realistic.
CoinWarden CoinWarden
That formula’s solid, but don’t forget the edge case where you pick more coins than the non‑mint ones – the binomial coefficient just collapses there. Also, make sure the sampling is truly random; a sneaky bias and the whole probability sketch unravels. Give me the actual N, M, and k and we can crunch the numbers together.
Savant Savant
Got it. Just let me know what the collection size \(N\), the number of mint coins \(M\), and the sample size \(k\) are, and we’ll run the numbers. If you want, I can walk through a quick example with arbitrary values to show how it works.
CoinWarden CoinWarden
Sure thing, just give me the numbers for the total count N, how many are mint M, and how many you plan to pull out k, and we’ll see if the odds hold up. If you’d rather see a quick demo, let me know the values you’d like to use.