Player A has a coin that lands heads with probability pa, and player B has a coin that lands heads with probability pp. Player A begins by tossing their coin; if it lands heads, they win. Otherwise, player B gets a chance to toss their coin; if their coin lands heads they win, otherwise the game moves back to player A. This continues until someone tosses a "heads"; this person is then crowned the winner. For notational convenience, you may leave your answers in terms of qA := 1 - PA and q8 :=1 - PB. wherever necessary. a. What is the probability that nobody is crowned the winner (i.e. the game continues to infinity)? b. What is the probability that A is crowned the winner? c. What is the probability that B is crowned the winner? d. Now, suppose that PA = pp:= p. Is it possible for A and B to have an equal chance at being crowned the winner? Provide some mathematical justification for your answer. 7 B I Ff T: SS