Question

If we flip 2 coins why would we consider the following: HH, HT, TH, and TT? Why doesn't HT and TH count as the same event?

Answer 1

Because they are two separate coins. (Imagine say a quarter and a nickel...)
You see, if coin one is H, coin two can be either H or T. If coin two is H, coin one can be H or T.

Coin (1) = (H) or (T)
Coin (2) = (H) or (T)

We do this to distinguish that there are 2 coins and that every outcome is different.

Answer 2

So getting a result with a heads and a tails happens half the time while the other two events happen only a quarter of the time. I guess if you didn't know that they were separate coins it would be confusing... Thanks lol.

Answer 3

Yes, the probability of getting a head and a tail is 1/2. While the probability of getting just heads or just tails is 1/4. The probability of getting at least one head or one tail however, is 3/4 because there is only one outcome where is don'e have a head or a tail respectively.