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Flipping Coins (Posted on 2004-10-13) Difficulty: 4 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution to First Question (high chance of error) | Comment 4 of 26 |
(In reply to Solution to First Question (high chance of error) by David Shin)

Doh.  Not thinking about it properly.  f(n) is the expected number of rounds to finish when starting with n heads, not coins.  Assuming I computed the values of f correctly, the solution becomes

p(0,5)*f(0)+p(1,5)*f(1)+...+p(5,5)*f(5).

I don't want to do this out...I wouldn't be surprised if it came out to something nice.


  Posted by David Shin on 2004-10-13 17:30:08
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