Samhita faces a three-headed dragon. She wins a 'Tactical medal' if she manages to defeat exactly one of the three heads.
The battle proceeds head-by-head under the following conditions:
The probability of defeating the first head is \(\dfrac{1}{3}\).
After a win: if she defeats a head, the probability of defeating the next head is \(\dfrac{2}{3}\).
After a loss: if she fails to defeat a head, the probability of defeating the next head is \(\dfrac{1}{4}\).
What is the probability that Samhita earns the 'Tactical medal'?

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.