If 8 fair coins are flipped, what are the odds that there will be more heads than tails?

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- Jun 19th 2010, 06:22 PMmathman88Coin Flip
If 8 fair coins are flipped, what are the odds that there will be more heads than tails?

- Jun 19th 2010, 06:40 PMSudharaka
- Jun 20th 2010, 06:59 AMawkward
I like

**Sudharaka**'s solution, but here is an alternative approach just to show there is more than one way. Let H be the number of heads, T the number of tails. Then

P(H < T) + P(H = T) + P(H > T) = 1

By symmetry, P(H < T) = P(H > T), so

2 P(H > T) + P(H = T) = 1

It's pretty easy to find P(H = T) because this is just the case H = T = 4. Then use the equation above to solve for P(H > T).