Probability vs Proportion

In this blog, I will explain the difference between probability and Proportion.

These are two different terms and concepts, but they must be clarified.

Because sometimes they overlap.

So sometimes, the probability and the Proportion are the same numbers.

And sometimes they are different numbers. It depends on the problem.

Sometimes it depends on the way you're asking the question and so on.

So, I'm going to start with the definition and then describe some examples.

So here are the distinctions.

• Probability is the likelihood of an event occurring or the likelihood that a statement is true.

• Proportion is a fraction of the whole.

So, what is the difference between them?

Example: let's start with an example of Dental hygiene.

I spend 5.1 minutes each day brushing my teeth out of 17 hours while awake.

So that's a total of 1020 minutes.

Now, I'm going to present three statements to you, and I would like you to consider which statements are factual and which are not. Based on this information.

1. The Proportion of my waking day spent brushing my teeth is 0.5 %.

2. The probability that a randomly selected minute of my day involves teeth brushing is 0.005.

3. The probability that I will brush my teeth during the day is 1.

If you think correctly, the answer is that all three statements are true.

So, the Proportion of my waking day spent brushing my teeth is just a fraction of my entire waking day.

All 17 hours that I'm awake.

I brush my teeth for one-half of one percent.

Now, notice that what's different between these statements is the exact phrasing of the statement.

So, the probability that a randomly selected minute out of my day vs. the likelihood that the event of teeth brushing during a day will occur.

So here we have another example.

This one is more fun.

It could be related to dental hygiene.

EXAMPLE: I eat 100 grams of chocolate every Friday.

So,

1. The Proportion of my week that contains a chocolate-eating day is one out of seven, which equals 0.143, which equals 14.3%.

2. The probability that a randomly selected day during the week involves chocolate eating is 1.

3. The probability that I will eat chocolate during the week is one.

All the above statements are true.

In fact, a general theme of statistics is that you can get significantly different answers from the same dataset, depending on exactly how you phrased the question. You'll see those come up quite often in real life.