Probability and Statistics > Probability > Probability frequency distribution

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Probability frequency distribution questions in statistics always have the term “frequency distribution” in the question. For example, the question might ask you to figure out the probability of a simple event happening, using a frequency distribution table. If you *don’t* have the phrase “frequency distribution” in the question, see other problem types in the probability index.

## Probability frequency distribution: Overview.

A probability frequency distribution is a way to show how often an event will happen. It also shows what the probability of each event happening is. A frequency distribution table can be created by hand, or you can make a frequency distribution table in Excel.

## Probability frequency distribution: Steps

**Sample question**: In a sample of 43 students:

- 15 had brown hair.
- 10 had black hair.
- 16 had blond hair.
- 2 had red hair.

Use a **frequency distribution table** to find the **probability** a person has neither red nor blond hair.

**Step 1: ** *Make a frequency distribution table.*

List the items in one column and the number of items in a second column. In this case, your items are hair colors: brown, black, blond, red.

**Tip:** If you have a large number of items, use tally marks to help you find the total.

**Step 2: ***Add up the totals*.

In the sample question we’re asked for the odds a person will **not** have blond or red hair. In other words, we want to know the **probability** of a person having black or brown hair. Note that you’re told in the question there are 43 students in the class.

Brown = 15/43 (15 out of 43 students have brown hair).

Black = 10/43 (10 out of 43 students have black hair).

Add these together to get the total number of students who have brown or black hair.

15/43 + 10/43 = **25/43** (25 out of 43 students have either brown or black hair).

You’re done with solving this Probability frequency distribution question!

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Frequency = total frequency * probability

This formula is needed for what? Please show the process

That’s a generic equation you could use for almost anything. For example, the number of heads you get in a coin toss would be 1 * .5 = .5. Or the odds of getting an ace if you draw twice (with replacement) from a deck of cards = 2 * 4/52.