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?

I think this is error free.

I enumerated all possibilities by hand for the first 3 rounds:

The exact probabilities for finishing in each of the first 3 rounds are:

1/32

211/1024

7431/32768

for a total of 15207/32768

or about .46408

My guess for the first part is 10 because for 1 coin the answer would be 2.

-Jer

 

Posted by Jer on 2004-10-13 17:46:16