Probability/Statistics question

[wewokahorn]

If a coin is flipped 50 times, what are the odds that the outcome will be exactly 25 heads and 25 tails? My daughter missed this question on her last exam - 50% chance was her answer.

 

[stupidgringo]

Seems like it would be close to 100% probability that it would be an even split, but what do I know I was a government major....

 

[Mal]

[50! / (25! * 25!)] / (2 ^ 50) = ~ 11.2 %

or

(50 choose 25) / (2 ^ 50)

Even in my disillusioned state, I'm fairly confident that's correct.

 

[RiceHorn04]

Mal is right,

It's a simple binomial distribution problem.

P(p, k, n) = [N! / (K! * (N-K) !) ] * P^K * (1-P)^(N-K)

Where:
P = probability of a success (a head in this case)
K = number of successes (25 here)
N = total number of trials (50 here)

In your case, this is:

50! / (25! * 25!) * (.5)^50 ~ 11.2%

 

[Luke Duke]

Mal is correct.

 

[SynTex]

according to Rozencrantz & Guildenstern Are Dead, it would be 0%, as you would have flipped heads 50 times in their weird universe.

 

[wewokahorn]

Thanks for the help guys. I still don't understand, but my daughter now sees the light.

 

[RiceHorn04]

In reply to:

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[ctrl+alt+del]

Man, y'all some smart sons o'*******! Math was and is my weakest subject. Damn numbers...

 

[CaboWabo]

NERDS!!!!!!!!!!!!!!!!!