Hi
So this is my problem:
Suppose you have a deck of N cards, each with a unique symbol (c1, c2, ... , cN). I draw a hand of m cards and note down each of the symbols on the cards. I then put these cards back in the deck and draw another hand, note down the cards and continue repeating. How many hands would I need to draw before the probability that I had seen all the cards is higher than a given probability value (p)?
I'm trying to write this without specifying values for my variables as I need to work this out for quite a few different scenarios, but to make myself clearer I'll give an example:
If I have 52 cards and repeatedly draw a hand of 4 cards, noting down which ones I've seen, how many hands do I have to draw before it is likely (i.e. p>0.5) that I have seen all the cards? How many would I have to draw before it is likely that I've seen 40 of them?
I'm not sure what distribution to use here as the trials are dependent, but any help or points in the right direction are appreciated.
So this is my problem:
Suppose you have a deck of N cards, each with a unique symbol (c1, c2, ... , cN). I draw a hand of m cards and note down each of the symbols on the cards. I then put these cards back in the deck and draw another hand, note down the cards and continue repeating. How many hands would I need to draw before the probability that I had seen all the cards is higher than a given probability value (p)?
I'm trying to write this without specifying values for my variables as I need to work this out for quite a few different scenarios, but to make myself clearer I'll give an example:
If I have 52 cards and repeatedly draw a hand of 4 cards, noting down which ones I've seen, how many hands do I have to draw before it is likely (i.e. p>0.5) that I have seen all the cards? How many would I have to draw before it is likely that I've seen 40 of them?
I'm not sure what distribution to use here as the trials are dependent, but any help or points in the right direction are appreciated.