Another Badminton Match

Level pending

Credit to Wee Xian Bin for the original problem .

Mark and Jolene are at it again. This time they are playing the badminton match such that whoever has 2 more set wins than the opposite player wins the game. If Mark still has a 0.4 0.4 chance of winning a set, then the probability that Jolene will win the entire match can be represented as a b \dfrac{a}{b} for coprime positive integers a , b a,b . What is a + b a+b ?


The answer is 22.

Daniel Liu by Daniel Liu , 21, USA

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1 solution

Kartik Prabhu
Jun 13, 2014

The probability that Jolene instantly wins is 0.36 0.36 , whilst the probability that they end up back on level pegging is 0.6 × 0.4 + 0.6 × 0.4 = 0.48 0.6 \times 0.4 + 0.6 \times 0.4 = 0.48 .

When they get back to level pegging, the probability that Jolene wins is the same as it was at the start.

Let's represent this probability with p.

p = 0.36 + 0.48 p p = 0.36 + 0.48p

0.52 p = 0.36 0.52p = 0.36

p = 36 52 = 9 13 p = \frac{36}{52} = \frac{9}{13}

So the answer is 9 + 13 = 22 9 + 13 = \boxed{22}

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