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I am wondering, how do I ago about calculating 1 in chances from a percentage?

Example:

  • A 1 in 2 chance is 50% and 0.5 as a decimal.

What I want to do:

  • I have the value 0.1431 (14.3%) and want to convert that into a 1 in chance - any help is much appreciated, thanks.
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  • $\begingroup$ $0.5 = 1/2$ is one chance over 2, so if the percentage is $x$ with $x=1/a$ .... $\endgroup$
    – nicomezi
    Sep 25, 2020 at 9:15
  • $\begingroup$ I think this is rather intuitive: For example $25~\%$ is "one in four", $5~\%$ is "one in 20" ... Can you guess how to calculate these numbers? It involves taking the inverse ... $\endgroup$
    – Matti P.
    Sep 25, 2020 at 9:16
  • $\begingroup$ Also, do you have requirements that the number should be an integer? Because, obviously, not all percentages (or fractions) can be written as "1 over an integer". For example $0.6667$ is $\frac{2}{3}$ ... $\endgroup$
    – Matti P.
    Sep 25, 2020 at 9:22
  • $\begingroup$ Thank you very much! So, from the first response, you divide 1 by the decimal if I am correct. For example: if I have 2%, I convert it into a decimal (0.02), then do 1/0.02, which equals 50 - giving the answer: 1 in 50 chance. $\endgroup$
    – user828171
    Sep 25, 2020 at 9:22
  • $\begingroup$ Not bad, but not intuitive enough. After you convert the percentage $(p)$ into a fraction (typically with a denominator = 100), you end up with an equation like $\frac{1}{n} = \frac{p}{100}.$ This is the intuition behind the math. Once you have stretched your intuition here, the math should fall into place. $\endgroup$
    – user2661923
    Sep 25, 2020 at 10:00

1 Answer 1

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A $1$ in $n$ chance can be written as $\frac{1}{n}$. This can be set equal to the probability in decimal form, $p$.

$$p=\frac{p}{1}=\frac{1}{n}$$

You should notice that you are simply finding the reciprocal of $p$ to find $n$. This means that if $p$ is a fraction, you can simply swap the numerator and denominator to get $n$.

Simply divide $1\div p$ to get $n$.

In this example, that means: $$n=1\div0.1431\approx\boxed{6.988}$$

So, $0.1431$ ($14.3\%$) is approximately a $1$ in $6.988$ chance.

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  • $\begingroup$ percentages can be tricky :-) $\endgroup$
    – FirstName LastName
    Jul 13, 2022 at 1:22

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