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?

You should add up the probability for the first three rounds; you just gave the probabiity for exactly three turns.  Your "expected" number at 3 was really "most likely."  Expected values are the probability weighted averages of all the possible outcomes.

Posted by bernie on 2004-10-14 20:33:27