Quick probability question

[jono]

with a 51.5% biased coin towards heads, what is the odds of having X more heads than tails in Y flips?

as an example, say X = 250 and Y = 4000. thanks!

[jay_shark]

In general Y>=x .

If we use your example x=250 and y=4000 then here is what you do .

P=0.515
q=.485

Number of heads + number of tails must equal 4000 .
Let k be the number of tails , then we have k+250 +k =4000
2k=3750
k=1875 Therefore you must have flipped 1875+250=2125 heads and 1875 tails .

4000C2125*0.515^2125*0.485^1875

[jono]

thanks jay