A trading card series has 200 different cards in it, which are sold in 5-card packages.
Each package has a random sampling of the cards (assume that any card of the 200 has an equal chance of being in a package).
On the average, how many packages will need to be bought to collect the complete series if...
A: all the cards in a package will always be different
B: a package can have repeats
For problem B, Charlie is correct that I said "(n-1)/200" when I should have said n/200.
The second "error" is really just another way of getting the same result. I gave a general formula for p(m,n) with a separate formula for the special case of p(m,200). This formula gives the probability that we had 199 at m-1 and have 200 at m. Charlie, instead, used the general formula to get the probability that we have 200 at time m (or earlier) and then subtracted the probability that we have 200 at time m-1 (or earlier).
Both methods give the same result, but Charlie's is a bit more elegant.
For problem A, my errors were greater. Yes, I got the denominator wrong and I also got the f(0,x) to f(5,x) reversed. As with problem B, I gave a special case for the end conditions and Charlie used the general formula at time "m" but subtracted the probability that 200 cards were already reached at time "m-1". In this case, Charlie's method is much more elegant.
So, if this problem has been answered by two different methods doesn't it count as solved?
my methods and Charlie's corrections
