So I have something that has a 1/128 chance of occurring, let's say. Suddenly, the chances of that thing happening are increased by 20%. How is that fraction written? Would you multiply 1/128 by 6/5 (yielding 3/320), or would you take 128, multiply it by 4/5, and then invert it (1/102)?
This isn't for homework, I'm merely curious.
Thank you
On
The first approach is correct.
Initial $p = \dfrac1{128}$, you need to increase $p$ by $20\%$
Note
Since $p = \dfrac1{128}$, i.e. in the form of a fraction, it is possible to obtain the correct result by manipulating its denominator only, but then you would need to divide the denominator by $1.2$,
i.e. multiply it by $\dfrac56$
Multiplying by $6/5=1.2$ is the correct approach. This increases a value by $20\%$. Multiplying by $4/5$ decreases a value by $20\%$, but inverting that is not the same as increasing by $20\%$. It results in multiplying by $5/4$, which is an increase of $25\%$. On top of that, $128 \cdot \frac 45=102.4,$ not $102$