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

A: First pack picked has 5 diff. cards. Next pack can fall into any of the following six categories :
1.With 0 new cards
2.With 1 new card
...
6. With 5 new cards

average # of new cards / pack = (1+2+3+4+5)/6 = 15/6 = 5/2

To get 195 more cards to complete 200, buy 195/5/2 = 78.

Hence, buy 78 + 1 = 79 total packs.

Posted by Keedom on 2002-11-18 23:59:16