[arrowsmith]

You're flipping pairs of coins until you get either "HT" or "TT". So the only two possibilities are:

1. keep flipping until you get HT (and so you choose 'heads') 2. keep flipping until you get TH (and so you choose 'tails')

Since HT and TH are equally likely, results 1 and 2 are equally likely, i.e. there's a 50% chance of choosing heads, 50% change of choosing tails.