Question

What is the relationship between probability and percentage?

Answer 1

The relationship between probability and percentage is the same as that of decimal and percentage. Since, the probability of an event cannot be greater than 1, its percentage cannot be greater than $100\%$. Also, both probability and percentage are a non-negative quantity. We will use an example to convert the probability into its percentage value.

Complete step by step solution:
We shall understand the relation between probability and percentage with the help of the following example:
Let us say there is an event ‘A’ such that the event has two possibilities. These are ‘P’ and ‘Q’ respectively. Let us say the probability of P occurring is 0.7 and the probability of ‘Q’ is 0.3 . We will convert these probabilities into their respective percentages and derive a general relation between the two quantities.
The percentage probability of ‘P’ occurring can be calculated as:
$\begin{aligned} & =\left( 0.7\times 100 \right)\% \\\ & =70\% \\\ \end{aligned}$
And, the percentage probability of ‘Q’ occurring can be calculated as:
$\begin{aligned} & =\left( 0.3\times 100 \right)\% \\\ & =30\% \\\ \end{aligned}$
So, from our above example, we can generalize that, if the probability of any event is ‘x’, then its percentage probability (say, ‘y’) can be given with the help of the formula:
$\Rightarrow y=\left( x\times 100 \right)\%$

Hence, the relationship between probability and percentage has been derived and is the same as a relation between a decimal and percentage.

Note:
We know that whenever we calculate the percentage of any quantity, that is, of a fraction or a decimal, it is always a non-negative term. This can also be understood from the fact that probability of any event is a non-negative entity. This fact can be used to verify our answer when we calculate the probability or percentage probability of any event in our problem.