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 re(2): computer-assisted solution by Vernon Lewis)

UBASIC does a good job of keeping track of the numerators and denominators of rational numbers.  The sum of the probabilities (in rational form) did come out to be 1 exactly and the divisions by 5 seem to work as well. I would trust the result, as there is more chance human calculation might make a carry error, etc., some place.

Posted by Charlie on 2007-07-24 10:27:27