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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

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

  1. Eva

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

  2. 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.