I have a question about the usage of fractions and percentages in questions related to probability. I am wondering if a fraction is the same as a percentage. To better explain my question, I will provide an example.
Suppose in a question about probability, we have worked out the probability of event $A$ occurring to be $\frac{1}{2}$ or $50 \%$.
Is it fine to write $P(A) = \frac{1}{2} = 50\%$? or $P(A)=\frac{1}{2}$? or $P(A)=50\%$?
I personally do not think equating a fraction and a percentage is a good practice, so I would like to know what is the standard notation.
$\endgroup$ 31 Answer
$\begingroup$Fractions are the common notation for discrete probabilities, since the denominator expresses the number of possibilities. For instance, in the roll of one fair six-sided die there are six possible outcomes, so it would be common practice to write $P[X = k] = \frac16$ for $k = 1, 2, ... 6$. When two dice are rolled, $P[X = 1] = \frac{1}{36}$ while $P[X = 2] = \frac{2}{36} = \frac{1}{18} $ and $P[X = 7] = \frac{6}{36} = \frac{1}{6} $ but the denominator of $36$ might be retained to represent total distinct die roll combinations, rather than reducing the fractions. As the number of outcomes becomes large, percentages might be preferred, and it could still make sense to write the fraction as the derivation of the decimal or percentage based on outcomes, thus showing both formats. This would be if you wanted to show the possible outcomes but continue calculations as decimals or percentages.
In continuous probability distributions, the probability is calculated by an integral and in most cases the result will be expressed as a decimal or a percentage.
I think that this is a good question because notation is often underrated.
$\endgroup$
