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Probability Question

M

ModelM

Member
I was thinking about coin flipping today and had a question I was wondering about. We all know that by flipping a coin, there is a 50% chance of getting heads, and a 50% chance of getting tails. Ideally, if you flip a coin 100 times, there should be 50 heads and 50 tails.

Obviously, this isn't always the case. So what is the probability of getting exactly 50 heads and exactly 50 tails after flipping a coin 100 times?
 
That would be [ (100!) / [(50!)(50!)] ] * (.5)^50 * (.5)^50 = 0.079589.

It's just the formula for binomial distributions. Assuming you have N number of trials, each of which has Y probability of 'success', the probability that you'll get X successes is:

(N choose X) * Y^X * (1-Y)^(N-X),

where (N choose X) = N!/[X!(N-X)!].

So in this case we can choose either heads or tails to be 'success', and the probabilty for either is .5, and we want 50 'successes', so... just plug the numbers in: N=100, Y=.5, X=50. 100 factorial is more than most calculators can handle (9.33x10^157).
 
If you want to get really technical, remember that most US coins are actually weighted to one side by very small amounts. That whould be the "Heads" side. So in reality the distrobution will not be 50/50. Ik, that ends our discusion of totaly useless trivia for the day. Please tuen in tommorow when we discuss the useless trivia about glass actually being a liquid.
 
To make things more complicated you could also factor in the slight chance that the coin would land and stay on it's edge 🙂
 
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