A fair coin is tossed repeatedly. Let $n > 1$. What is the probability that a head will occur for the second time on the $n$th toss?
I have considered conditional probability, and got $\frac 12$, but the question is 6 marks and this seemed too straightforward.
I then considered sampling, and deduced that order doesn't matter and repetition is allowed, but wasn't sure if this was the correct way to go.
Any help is appreciated
There are 2 necessary components for the second heads to come up on the $n$th toss. First, you have to have exactly 1 head come up in the first $n-1$ tosses. Next, you have to have a head on the $n$th toss. The probability of the second head on the $n$th toss is a product of these probabilities. The second one clearly is 1/2. What is the probability of the first requirement?