a football match is played between Team 1 and Team 2. The probability that team 1 wins is and the for team 2 to win the probability is ; finally to draw is . In the event of a draw the two teams must play a rematch with the same probabilities as before. In the event of a second draw there is a penelty shoot out whith each team having a 50% chance of winning.
In terms of and what is the probability that Team 1 defeats Team 2?
Letting T1, T2 and D be the events of Team 1 winning, Team 2 winning and a draw respectively. I draw a tree diagram and deduce that which is equal therefore to
p + p(1 - p - q) + 0.5(1 - p - q)(1 - p - q). There are further questions but I don't feel confident that my answer is correct....
Thanks for any help in advance.