Solving Complex Probability Problems: Example Walkthrough for Opposite Events

Hi. I would like to ask for clarification regarding the above-mentioned subject.

Step 5: Probability and Statistics
Course 3/5: Solving Complex Probability Problems
Slide 3/10

" Event A (it takes three flips or more for a coin to land heads up) ."

My understanding is that we’ll get our first head on the third flip.

I understand the concept of opposite events. We solved for the opposite events, the probability of getting a head on first and second flip, which gave us 0.75.

What I can’t understand is applying the concept of opposite set will be the final answer, which is 0.25.

0.25 is the probability that we won’t get any head on the first 2 flips, but for getting a head on the third flip, won’t we consider the probability of getting a head in the third flip (cause it may be a tail, right? idk)

So I’m multiplying 0.25 by 0.5.

I just want to understand fully why we stopped at the probability of not getting a head on the first 2 flips without considering the third one will be a head.

Thank you in advance.