@markr,
Izzie and Try are going to have a duel where they alternate shots - Izzie goes first - until one is hit.
The probability of Izzie hitting her target is always 1/7.
Try has the unique ability to set his probability (anything between 0 and 1) ahead of time - it remains constant after it is set.
Being the gentleman that he is, Try selects a value that gives each of them a 50/50 chance for survival.
What probability does Try select for himself? In other words, to make it a fair duel, what is the probability of Try hitting his target on each shot?
Try, overcome at the thought of pumping one into Izzie, elects to play Russian Roulette with a 6 gun that he hands to Izzie for her to use on herself lest she miss. Meanwhile, Try stands to attention in the firing line, in the fervent hope that she gets two shots off.