Question

Sue and Mary agree to play the best of three games of badminton. They stop if either of them have won two games. Over a long period of time, Sue wins 4 games out of every 5 games they play. Find the probability that Sue will win the best of three.

I have that the chance of winning best of three is 0.50 but not sure what next.?

Answer 1

Prob(m) = 1/5
prob(S) = 4/5

Possible outcomes in best of three"
MM --- (1/5)(1/5) = 1/25
MSM -- ((1/5)(4/5)(1/5) = 4/125
SMM -- ((4/5)(1/5)(1/5) = 4/125
SS ---- (4/5)(4/5) = 16/25 ----> Sue wins
SMS -- (4/5)(1/5)(4/5) = 16/125 ----> Sue wins
MSS -- ((1/5)(4/5)(4/5) = 16/125---> Sue wins

prob(sue wins) = 16/25+16/125+16/125 = 112/125 or .896

add them up to get 1 as a check
you said "I have that the chance of winning best of three is 0.50"
How so ??