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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How do you solve this problem:

52% of business travelers plan their trips less than two weeks before departure. The study is replicated in the tri-state area with a sample of 122 frwquent business travelers. Develop a probabilty distribution for the number of travelers who plan their trip within two weeks of departure.

Thanks

Hi, Thomas,

Can you post this question on the forum? One of our moderators will be happy to answer stats questions :)

Thanks for dropping by!

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.