to find the probability of a biased coin?

my ques is a bit different one, i don't want to know the probability of throwing coin n times or knowing the probability of biased flipping x times. i want to know the probability p of head, if a coin is biased, i want know the algorithm to find the value of 'p'. how can i find the value of p, whether it is .1 or .4 or .5, i don't know, i want to find this. i want to know the algorithm for this. please explain by elaborating everything

• You want to find $p$ from what information? – martini Oct 24 '12 at 13:02
• this is the information, i want to find the algo that in how many flips i can probably find the value of p. as if get 1 head in 10 flips, do i say that it has p =.1, what has to be the algo so that i can find p – Amritpal Singh Oct 24 '12 at 13:08

You can never do enough flips to know $p$ exactly. One estimate you could make is to throw the coin "a lot" of times, then estimate $p$ as the fraction of heads you get. If you did $N$ flips and got $pN$ heads, this will maximize $p^{Np}(1-p)^{N(1-p)}{N \choose Np}$, the chance that if the heads probability is $p$ you got this many heads. There is a subtle difference between the chance that you got this many heads given $p$ and the chance of $p$ given this many heads, but you shouldn't be far wrong.
• To find $p$ you need to use the observation of how many heads you got. So $p$ is just the ratio of heads to total throws. There is no magic $N$, your accuracy gets better and better (on average). – Ross Millikan Oct 24 '12 at 13:39