Answer: ![\frac{n-m}{n}](https://tex.z-dn.net/?f=%5Cfrac%7Bn-m%7D%7Bn%7D)
This is the same as writing (n-m)/n
Don't forget about the parenthesis if you go with the second option.
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Explanation:
The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.
For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.
The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.
We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".
Doing a bit of algebra would have these steps
![1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\](https://tex.z-dn.net/?f=1%20-%20%5Cfrac%7Bm%7D%7Bn%7D%5C%5C%5C%5C%5Cfrac%7Bn%7D%7Bn%7D%20-%20%5Cfrac%7Bm%7D%7Bn%7D%5C%5C%5C%5C%5Cfrac%7Bn-m%7D%7Bn%7D%5C%5C%5C%5C)
and now the expression is one single fraction.