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May 20th, 2015, 04:57 AM  #1 
Newbie Joined: May 2015 From: New York Posts: 2 Thanks: 0  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? Thanks 
May 20th, 2015, 05:07 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,331 Thanks: 2457 Math Focus: Mainly analysis and algebra 
First calculate the number of heads you need to be in profit. Then use the binomial theorem to determine the probability of that event.

May 20th, 2015, 05:17 AM  #3 
Newbie Joined: May 2015 From: New York Posts: 2 Thanks: 0 
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?

May 20th, 2015, 05:50 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
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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