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

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