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

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

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Answer 1 · 2017-10-17T05:31:19

$\frac{5}{3}$ $5/3$

Explanation:

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

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

$1 - P \cdot$ $1-Pcolor(white)(*)$ is the probability of the event not occurring.

The odds will then be:

$\frac{P}{1 - P} \Rightarrow \frac{\frac{5}{8}}{1 - (\frac{5}{8})} = \frac{\frac{5}{8}}{\frac{3}{8}} = \frac{5}{3}$ $P/(1-P)=> (5/8)/(1-(5/8))= (5/8)/(3/8)= 5/3$

To make this clearer:

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

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

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

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

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