So the question is:
100 coins are tossed, what is the probability that exactly 50 are heads?
Now the answer is... there are 2^100 outcomes
and 100_C_50 of those outcomes have exactly 50 heads (using generating functions for example)
Hence the probability is 100_C_50/2^100 which is approximately 0.08
But what I don't understand is that why does order matter in this question? Why isn't the answer 1/101. You see there are 101 distinct sets' of outcomes. 1 set is all heads, 1 set is all heads except one, ..., 1 set is all tails. Among these sets, there is one where 50 are heads and 50 are tails.
Hence that is 1 set out of 101 sets. So the answer would be 1/101.
What is wrong with this reasoning?
If instead of 100 coinS, it was one coin tossed 100 times--would the answer still be 100_C_50/2^100?
Please help me, I was never taught probability in school and trying to learn it on my own!