You play a coin flipping game with 5 coins. On round 1 you flip all of them. On round 2, you pick up all the ones that came up tails (leaving all the heads alone) and flip them again. You continue to do this until all the coins are heads. For example:

Round 1:  H T T H T
Round 2:  - H T - H
Round 3:  - - T - -
Round 4:  - - T - -
Round 5:  - - H - -

Done in 5 Rounds.

What is the expected number of rounds you'll need to finish the game?
What is the probability you will finish the game in 3 rounds or less?

(In reply to About the expected value by Charlie)

Ahh, ok, I understand now. Thank you Charlie.

I went "discretely" through each round, and determined the chance of finishing in that round and then looked to see which had the highest chances (I had to make sure to keep going a little until my chances started to decrease).

The other way you guys were approaching it was to determine the non-discrete expected number of rounds. Almost like saying "most families have 1.5 children" when of course no one has 1.5 children.

So if you guys found 3.79… to be the expected number of rounds needed for the game to end, if you had to name an integer number of rounds as the expected value, would it be 3 or 4? It’s closer to 4, but I don’t know if that makes a difference.

Cool.

Posted by nikki on 2004-10-15 13:14:39