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Probabilities and odds

Odds are sometimes used instead of probability as a measure of chance. For example, suppose you are told that the odds of catching flu this year are 200:1 (read "two-hundred to one"). The sizes of the numbers on either side of the colon represent the relative chances of not catching flu (on the left) and catching flu (on the right). In other words, what you are told is that the chance of not catching flu is 200 times as great as the chance of catching flu.

Odds are usually presented in terms of whole numbers. So if you want to say that the chance of Lee losing the election is two and a half times as great as the chance of him winning, you would express this by saying that the odds of Lee winning are 5:2. The number on the left (the chance of him losing) is two and a half times bigger than the number on the right (the chance of him winning).

Note that odds of 10:1 are not the same as a probability of 1/10. If an event has a probability of 1/10, then the probability of the event not happening is 9/10. So the chance of the event not happening is nine times as great as the chance of the event happening; the odds are 9:1.

• Self-test questions:

1. What are the odds that tossing a fair coin will produce heads?
2. What are the odds that rolling a fair die will produce a 6?
3. Suppose the odds of the horse Blaise winning the 8 o'clock race at Happy Valley are 25:1 (and suppose that this actually represents the chance that the horse will win). What is the probability that Blaise will win?
4. If the odds of Lee winning the election are 5:2, what is the probability of him winning?
5. If the odds of an event are x:y, what is its probability?

• Answers

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Next: [T1.4 Combining probabilities] Up:[T1 What are the] Previous: [T1.2 Representing probabilities]
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