Question

Suppose that the only reasonable contenders for the NCAA championship are Villanova, Duke, and Michigan. You read on an online article that the odds are 3:1 against Michigan and 5:1 against Duke, what are the odds in favor of Villanova?

Answer 1

if odds in favour = a:b

ratio of winning = a / (a+b)

3:1 odds against michigan

therefore, 1:3 odd in favour of michigan

ratio of matches won by michigan = 1/(1+3) = 1/4

5:1 odds against duke

therefore, 1:5 odd in favour of duke

ratio of matches won by duke = 1/(1+5) = 1/6

therefore ratio of matches won by villanova = 1 - 1/4 - 1/6

= 24/24 - 6/24 - 4/24

= 14/24

odds of winning for villanova = 14 : (24-14)

= 14 : 10

odds of winning for villanova = 14 : 10

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