Probability Frequency Distribution: How to Solve Problems in Easy Steps

Probability frequency distribution questions 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 distributi

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