Here, I concluded that since the coin is biased, we don’t know what combination of heads and tails (for both flips) would give us 1/4. Is that not enough to conclude that D is the answer?
You do.
Do you mean we have to solve for H using algebra (like we did in the question) to conclude that?
Correct. You know there has to be (at most) two solutions as you’ll end up with a quadratic. Now it could well be that the solutions of the quadratic are both more/less than 1/5, in which case the answer will not be D.
Okay yes, that makes sense. Thanks Leaderboard!