Coin toss problem

[Alan Forrester]

Hello

Suppose that I have a coin and that when I toss is the probability of
getting heads is 0.5 and the probability of getting tails is 0.5. I
toss the coin according to the following rules. If I get more tails
than heads I stop tossing. Otherwise I toss the coin some fixed number
of times - N. Does anyone know of a good way to work out the
probability of getting heads?

Thanks,
Alan Forrester

[michael.h...@gmail.com]

You just stated that the probability of getting heads is 0.5. Please clarify your question. Perhaps what you mean to ask is: "What is the probability of the process terminating with fewer than N tosses?"

[danh...@yahoo.com]

You get a head if the first toss is a head (prob=1/2) or if the first
toss is a tail and the next N tosses are not all tails
(prob=0.5*(1-0.5^N)). These are mutually exclusive so add them to get
the answer.