As with your proof of immortality, we do not have sufficient information to begin to determine that. To make the calculation, we would need to know the proportion of pennies that are two-headed, and the proportion that are two-tailed. We know that P(H|D)=1 and P(H|F)=0.5, where D is a double headed and F a fair coin; but we cannot calculate P(D|H) from these without knowing P(D) - and, of course, P(T) (where T is a double tailed coin), because F =/= ~D. And, finally, the observation that the penny comes up heads tells us very little except that P(T|H)=0.
It's actually a pretty good analogy for your proof of immortality. You've taken two outcomes that aren't logical complements, made an observation that doesn't help to distinguish between them in any way whatsoever, failed to offer any information on the data that would allow a valid deduction to be made, and then asked what the answer is. The only sensible answer is "insufficient data provided".
Dave