# How do you find the odds of an event occurring given its probability 5/8?

Oct 17, 2017

$\frac{5}{3}$

#### Explanation:

Odds is the ratio of favourable outcomes to non-favourable outcomes:

If P is the probability of an event occurring, then:

$1 - P \textcolor{w h i t e}{\cdot}$ is the probability of the event not occurring.

The odds will then be:

$\frac{P}{1 - P} \implies \frac{\frac{5}{8}}{1 - \left(\frac{5}{8}\right)} = \frac{\frac{5}{8}}{\frac{3}{8}} = \frac{5}{3}$

To make this clearer:

The probability of throwing a 6 with a standard die is $\frac{1}{6}$

The odds of throwing a 6 are $\frac{1}{5}$

$\frac{P}{1 - P} = \frac{\frac{1}{6}}{1 - \left(\frac{1}{6}\right)} = \frac{\frac{1}{6}}{\frac{5}{6}} = \frac{1}{5}$