At each trial of a game, Don and Greg flip biased coins, simultaneously but independently. For each trial, the probability of heads is pD and pG for Don and Greg, respectively.

a - Given that the flips on a particular trial resulted in 2 heads, find the PMF of the number of additional trials up to and including the next trial on which 2 heads result.

b - Given that the flips on a particular trial resulted in at least one head, find the probability that Don flipped a head on that trial.

c - Starting from a trial on which no heads result, find the probability that Don's next flip of a head will occur before Greg's next flip of a head.

d - Given that Don receives $d for each head he flips, and Greg receives $g for each head he flips, find the transform associated with the total amount of money earned by the two players during the first n trials.