Question

A coin is flipped three times. How does P(H, H, H) compare to P(H, T, H)?

Answer 1

P(H,H,H)=P(H,T,H)

This is classical probability, so the probability of an event is the number of "favorable" events over total events.

The total number of events, by the counting principle, is 2^3=8.
The total number of events remains the same for P(H,H,H) and P(H,T,H), as you're still flipping 3 coins with two sides.

For P(H,H,H) the favorable event is (H,H,H) so 1, for P(H,T,H) the favorable event is (H,T,H) also one.

Conclusion:

P(H,H,H)=P(H,T,H)=1/8