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 re(2): About the expected value by Charlie)

Technically the expected value is an integral, not "average over large number of trials."  The later is a theorem: Strong Law of Large Number, which requires several regularity conditions.  The formal definition of an expected value is ¡ìX(£s)dP(£s) for all £s in £[, and P(£s) is the probability measure, while X is a function (the random variable) mapping each event £s into a number.

 

Posted by Bon on 2004-10-23 05:09:29