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if an event has probability $\pi$ and the other event has probability $1-\pi$. is there a mathematical name or label for the ratio of those probabilities, $\frac{\pi}{1-\pi}$?

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    $\begingroup$ How can an event have probability $\pi> 1$ ? $\endgroup$ Aug 21, 2021 at 23:19
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    $\begingroup$ I might be mistaken but I think it's called the odd. $\endgroup$
    – dezdichado
    Aug 21, 2021 at 23:20
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    $\begingroup$ Yes, this is called odds; it is often used in gambling. $\endgroup$
    – angryavian
    Aug 21, 2021 at 23:23
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    $\begingroup$ @AdamRubinson $\pi$ here is a variable representing a quantity in $[0,1]$, not $\pi \approx 3.14159\ldots$. $\endgroup$
    – angryavian
    Aug 21, 2021 at 23:24

1 Answer 1

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If $\pi$ is the probability of some event $E$, then the ratio $\frac{\pi}{1-\pi}$ is called the odds.

The higher the odds the more likely $E$ is to occur. You usually express odds in terms of a ratio of the denominator.

Examples:

$\pi = 1/2$ gives even odds or $1:1$ odds.

$\pi = 2/3$ gives $2:1$ odds.

$\pi = 1/3$ gives $2:1$ odds against

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