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

1st pack: you get an average of 3 diff. cards. 197 more to go to complete the series.

a pack may have all same - all different , each withy prob. 1/5.

u may get 0 - 5 new cards per pack , but since cards may repeat in a pack , these probs are weighted.

average # of new cards per pack =
(1*1 + 2*4/5 + 3*3/5 + 4*2/5 + 5*1/5 )/6 = 7/6.

to complete 197 new cards , 197/7/6 = 197*6/7 = 169 approx.

total # of packs = 169 + 1 = 170

Posted by Keedom on 2002-11-19 00:26:36