Consider a deck of 10 cards numbered in order from 1 to 10. Pick up the first five cards (1 to 5). Randomly discard one and take the 6. Randomly discard one again and take the 7. Continue until the 10 has just been taken.

a) What is the expected average of the five cards in the final hand?
b) What is the expected value of the smallest card in the final hand?

Recompute parts a) and b) where you still hold 5 cards, but go all the way through a 100 card deck.

(In reply to computer-assisted solution by Charlie)

For those interested, the exact rational solution for part a for 100 cards is

96 +

3138550867693340381917894711603833208051177722232017256448 

/

2524354896707237777317531408904915934954260592348873615264892578125

Posted by Charlie on 2007-07-24 00:06:53