How can I convert this percentage into odds?
How can I convert the percentage 0.000007151123842% into odds, so the outcome would be 1 in 13983816. Basically, I am looking for a way to convert any positive percentage into odds so the outcome gives me 1 in N.
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$\begingroup$To convert something to be "1 in N", you simply take the reciprocal. In this case, you have it correct:
$$ \frac{1}{0.00000007151123842} = 13,983,816 $$
So you get an event that happens "1 in 13,983,816" tries.
Odds are a bit different in that they usually give the ratio between two events happening. For example 1:1 (pronounced "1 to 1") odds means a 50% chance of that event happening and is equivalent to "1 in 2". A 20% chance would be 1:4. So, you'll subtract 1 from the reciprocal to get odds of 1:13,983,815.
In general, the odds are
$$ 1:\bigg(\frac{1}{p}-1\bigg) $$
where $p$ is the probability of the event expressed as a decimal.
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