Odds in statistics and Odds in a horse race

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Definition of Odds in statistics

[math]\displaystyle{ Odds=\frac{probability\ that\ the\ outcome\ occurs}{probability\ that\ the\ outcome\ does\ not\ occur} }[/math]

Example of a horse rase

Assumption

In order to simplify, the bookmaker in the following scenario does not charge any betting fees

A race that 5 horses start and 10 bettors bet

Here is a horse race that 5 horses start and 10 people ---10 bettors--- bet each of 5 horses.

Names of horses are A, B, C, D and E.

Horses
A
B
C
D
E