The chance of success in each trial is p.If p(k) is the probability that there are even number of successes in k trials prove that p(k)= p {p(k-1)}(1-2p)

Are you sure you have this right? From what you wrote if p > 0.5 then your value for p(k) becomes negative, which would be incorrect.

Thanks EBAINES for answering... this question is given to me as an assignment but I couldn't find a solution... I'm too confused

Is this the formula you were given:

p(k) = p(k-1) p (1-2p)?

It's pretty easy to show that this is incorrect. If p = 1/2 (such as in flipping a coin and getting heads), it says the odds of getting an even number of heads in, say, 2 flips of the coin is 0. Whoever gave you this formula was wrong.

oh! sorry. Its p(k)= p + {p(k-1)}(1-2p)... I missed the '+' sign in my question