Probability that heads never follows tails?

Question

Suppose a coin is tossed n times. H(i) is the event that the ith toss is heads, T(i) is the even that the ith toss is tails, and S is the event that H never follows T.

What's the probability of S in terms of n?

Answer 1

There are 3 possibilities.

All of the n tosses result in heads.

All of the n tosses result in tails.

There are k heads followed by (n-k) tails.

Probability of n heads = p^n

Probability of n tails = p^n

P(r=k)= nCk p^k (1-p)^(n-k) --- (case 3)

We can assume p=1/2 if the coin is fair.