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 A Coin Game (Posted on 2004-05-20)
Alex flips a fair coin 20 times. Bert spins a fair coin 21 times. Bert wins if he gets more heads than Alex, else Alex wins. Note that Alex wins if there is a tie. What is the probability that Bert wins?

 See The Solution Submitted by Brian Smith Rating: 3.5000 (4 votes)

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 re: Solution | Comment 7 of 12 |
(In reply to Solution by Gururaj)

Gururaj,
I agree with you...
I made up a full probability distribution table and the contrasted all possible outcomes.
The probability of any one outcome for Alex: 0.5^20
multiplied by the number of combinations of that many heads out of the 20 spins: (20 C x).
As for Bert: 0.5^21 and (21 C x).
It was then a matter of contrasting these against each other and summing for a total probablility of a win for each player.
The final answer... they both have a 0.5 chance of winning.
 Posted by Popstar Dave on 2004-05-23 02:59:13

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