Probability

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 $\frac{\mathbf{1}}{\mathbf{3}}$.




• After a win: if she defeats a head, the probability of defeating the next head is $\frac{2}{3}$.




• After a loss: if she fails to defeat a head, the probability of defeating the next head is $\frac{\mathbf{1}}{\mathbf{4}}$.

What is the probability that Samhita earns the "Tactical medal"?