Thread: probability help

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.

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

Originally Posted by Curious_eager

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

Hey,

Can you explain your working? Cause I know what the right answers are but dont know how to get to them.

Also the answers for c and d shown on my book is 0.0675 and 0.203 respectively.

thanks!

Originally Posted by Tweety

Hey,

Can you explain your working? Cause I know what the right answers are but dont know how to get to them.

Also the answers for c and d shown on my book is 0.0675 and 0.203 respectively.

?

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

Thanks a lot for correcting me. I missed that earlier.