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 To bernie by nikki)

About the 3.79...,

Suppose you keep doing the experiment over and over again.  Say the first time it took 5 turns to complete the set of heads, and the second time, it took 4 turns, and on successive tries it took 2, 7, 4, 2, 3, 9, 4, 2, 5, 3, 4, 4, 3, 2, 1, 2, 3, 5, 4, 3, 3, 4 and 3 turns in the first 25 times you try this experiment.  The average number of times that it took was 3.64 in this case.

In the long run, the average number of turns it would take to complete a set of 5 heads would be that 3.79... number.  The definition of "expected value" is just the average value it would have over the long run.

Posted by Charlie on 2004-10-15 03:56:13