Odds: Refresher

Written by Nate Soares, Eliezer Yudkowsky, et al. last updated
Requires: Math 1, Odds

Let's say that, in a certain forest, there are 2 sick trees for every 3 healthy trees. We can then say that the odds of a tree being sick (as opposed to healthy) are

Odds express relative chances. Saying "There's 2 sick trees for every 3 healthy trees" is the same as saying "There's 10 sick trees for every 15 healthy trees." If the original odds are we can multiply by a positive number and get a set of equivalent odds

If there's 2 sick trees for every 3 healthy trees, and every tree is either sick or healthy, then the probability of randomly picking a sick tree from among all trees is 2/(2+3):

Odds v probabilities

If the set of possibilities are mutually exclusive and exhaustive, then the probabilities should sum to If there's no further possibilities we can convert the relative odds into the probabilities The process of dividing each term by the sum of terms, to turn a set of proportional odds into probabilities that sum to 1, is called normalization.

When there are only two terms and in the odds, they can be expressed as a single ratio An odds ratio of refers to odds of or, equivalently, odds of Odds of are sometimes called odds ratios, where it is understood that the actual ratio is

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