I have a confusion about probability. I know my reasoning is wrong but I can't figure out why it's wrong. Can someone please clarify.
If I flip a coin once, the probability that it lands heads is $\frac{1}{2}$. If I flip it again, the probability is again $\frac{1}{2}$. These are independent events so I can find out the probability that I either the first one or the second one is heads by adding them up. So, I get $\frac{1}{2} + \frac{1}{2} = 1$. (reductio ad absurdum:) This can be extended to three flips where probability becomes $\frac{3}{2}$.
p.s. I know we need to do $\{HH, HT, TH, TT\}$ for correct answer but what's wrong with the reasoning above?