Following Unfair coins at South Park Elementary
Wendy and Sally have another friend, called Timmy. Although Timmy has no coin, he wants to play this game in a fair condition with them. Wendy does the first coin flip then Sally does. Is it possible to play this game in a fair way for Timmy, even without him having a coin? If so, what should be the values of $p_1$ (Wendy's coin shows head probability) and $p_2$ (Sally's Head probability) that make this game a fair game for all of them?
Note: Timmy cannot use Sally's or Wendy's coin and one of them wins at the end!