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May 20th, 2015, 05:57 AM   #1
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coin toss problem

Hey all. New to the thread and was looking for help with the following:

Suppose I toss a fair coin in a game where heads means I win 1.25 and tails means I lose 1.00. How would I calculate the probability that I would show a profit after X (100 for example) number of tosses?

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May 20th, 2015, 06:07 AM   #2
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First calculate the number of heads you need to be in profit. Then use the binomial theorem to determine the probability of that event.
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May 20th, 2015, 06:17 AM   #3
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Thanks for the reply. Not sure how to use binomial theorem. I've determined that for 100 tosses I would need minimum of 45 heads. How to proceed?
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May 20th, 2015, 06:50 AM   #4
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You want to find w such that 1.25w = 1(X - w) or w = 4X/9. You're looking for the probability that you get more than w wins:
$$
2^{-X}\sum_{k=\lfloor4X/9\rfloor+1}^X{k\choose X}.
$$

For X = 100 I get 68482723177360620218041365161/79228162514264337593543950336 or about 86.4%.
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