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Statistics / Fundamentals of Probability, with Stochastic Processes 3 / Chapter 1.4 / Problem 6

Fundamentals of Probability, with Stochastic Processes | 3rd Edition | ISBN: 9780131453401 | Authors: Saeed Ghahramani

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In a horse race, the odds in favor of the first horse

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QUESTION:

In a horse race, the odds in favor of the first horse winning in an 8-horse race are 2 to 5. The odds against the second horse winning are 7 to 3. What is the probability that one of these horses will win?

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QUESTION:

In a horse race, the odds in favor of the first horse winning in an 8-horse race are 2 to 5. The odds against the second horse winning are 7 to 3. What is the probability that one of these horses will win?

ANSWER:

Step 1 of 3

Odds can be interpreted as equally likely outcomes. If odds in favour of event are there are equally likely outcomes in which occurs, and equally likely other events (where does not occur). equally likely events in of which occurs.

Odds against event can be interpreted as odds in favor of its complement.

Events and odds:

- the first horse wins the race, odds in favor

- the 2 nd horse wins the race, odds against .

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