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Probability frequency distribution: How to solve problems

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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

Tally marks in a frequency distribution table.

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.
probability frequency distribution
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!


If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Probability frequency distribution: How to solve problems was last modified: January 10th, 2018 by Stephanie

4 thoughts on “Probability frequency distribution: How to solve problems

  1. Thomas

    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.


  2. Andale

    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!

  3. Eva

    Frequency = total frequency * probability
    This formula is needed for what? Please show the process

  4. Andale

    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.