I think it should be like this:-
a) 0.25 . 0.25 .0.25 = 1/64
b) 0.45 . 0.45 . 0.45 = 729/8000
c) 9/400
d) 27/800
Thanks,
Anshu
Paul and Gill decide to play a board game. The probability that Paul wins the game is 0.25 and the probability that Gill wins is 0.3. They decide to play three games. Given that the results of successive games are independent, find the probability that
a Paul wins three games in a row,b all games are drawn,c Gill wins two games and Paul wins one game,d each player wins just one game each.
A tree diagram would probably be your best bet:
c) 3(0.25*0.3^2) =0.0675. This is because there are three identical ways of Paul winning and Gill winning two (it's clearer on a tree diagram)
d) d each player wins just one game each.
6(0.25*0.3*0.45) = 0.2025. This is because Paul must win one, Gill must win one and one must be a draw. Following the branches there are 6 ways this can happen