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Racing Odds

Age 11 to 14
Challenge Level Yellow star
  • Problem
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This is a nice solution from Andrei of School 205 Bucharest. Thank you Andrei.

Looking at the first race.

If the odds are 2 to 1 against the rhinoceros, then the probability that the rhinoceros will win is 1/(1 + 2) = 1/3. For the hippopotamus, the probability that he will win is 2/(2 + 3) = 2/5.

The total probability (that there is a winner) is 1. So, the probability that the elephant will win is:

1 -1/3 -2/5 = 4/15

So, the odds for him are 11 to 4 against the elephant.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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