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
define
E to be the expectation of
different cards in 5 card package
f(x) to be the average increase
in distinct cards when the person
already has x and buys another package
C(x) to be the average number
of distinct cards after x
packages
then
C(0) = 0
C(n) = C(n-1) + f(C(n-1))
f(x) = E*(200 - n) / 200
the only difference between
case A and B is E, the rest is
the same
E(A) = 5
E(B) = 4.95 (to 3 dec. places)
the answer is to find
n such that C(n) = 200
i dont think this can be done
analitically. numerically
however the answer is
An = 237
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