The outcome of the third flip of the coin is independent of the results of the first two flips. A fair penny has two possible outcomes: heads (H) or tails (T).
The probability of landing heads on a single flip of the penny is:
\[ P(H) = \frac{1}{2} \]
Therefore, regardless of what happened in the first two flips, the probability that the penny lands on heads on the third flip is:
\[ \frac{1}{2} \]
To express this as a fraction in simplest form, it is already in simplest form:
\[ \frac{1}{2} \]
Thus, the answer is:
\[ \frac{1}{2} \]