if a coin be tossed n times then probability that the head comes odd times?

When n = 1 , clearly the probability that the head comes odd times is 1/2 .

Assume that when n = k the probability that the head comes odd times is 1/2 .

When n = k+1 , if the head comes odd times then there are two cases .

Case1. The head comes odd times in k tosses and the tail comes on the (k+1)th toss

The probability of it is (1/2) * (1/2) = 1/4 .

Case2. The head comes even times in k tosses and the head comes on the (k+1)th toss

The probability of it is (1 - 1/2) * (1/2) = 1/4 .

So the probability that the head comes odd times is 1/4 + 1/4 = 1/2 when n = k+1 .

Therefore , the probability that the head comes odd times is 1/2 for any n .

Well a coin goes 49/51 believe it or not depending on the starting side. And the only way an answer can be formed if there was an amount the coin was flipped. .50nx.50=x