I'm reading high school probability, and this doubt arose while reading about successive coin tosses.
Suppose I'm tossing an unbiased coin, and recording the outcomes. Let's say that by pure chance, I get 'n' consecutive heads. I'm confused about the probability of the (n+1)th coin toss.
When I asked my teacher this, she said that the probability of any (unbiased) coin toss will always be 1/2, regardless of the previous outcomes, as each toss is an independent event. This does make sense to me, but there's a further question.
Since the statistics have to balance out, i.e. after a considerable number of tosses the head-tail ratio should reach close to 1/2, isn't the probability of getting a tail also increasing, with each successive head that we get?
If not, and the probability of each coin toss is indeed 1/2, then what's changing as we keep getting heads?