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**Is it true**

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

I've already prove the case when n is odd, then I used induction to prove this , the calculation is tiresome , not sure it's right tho.

*Last edited by Stanley_Marsh (2007-04-10 10:42:08)*

Numbers are the essence of the Universe

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

K=odd , this holds, if k= even ,this holds too , then throw n dices , the probability of getting an even sum will be 0.5

*Last edited by Stanley_Marsh (2007-04-10 10:42:38)*

Numbers are the essence of the Universe

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**whatismath****Member**- Registered: 2007-04-10
- Posts: 19

You could see it this way:

denote nCk = (n choose k)

The Binomial Theorem says

(1+x)^n = summation (k=0 to k=n) nCk(x^k)

Put x=-1: 0 = summation (k=0 to k=n) (-1)^k(nCk)

So sum of odd terms = sum of even terms.

Put x=1 to see both sums are 2^(n-1).

With this we could see the probability questionthis way:

Prob(sum of n dice is odd)

= 1/(2^n) (# of combinations in which an odd number of dice is odd)

= 1/(2^n) (nC1 + nC3 + nC5 + ...)

= 1/(2^n) (2^(n-1))

= 1/2

Similar for the even case.

Thanks.

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

My proof works either , I just need to prove the case when n=even

Numbers are the essence of the Universe

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