5 Real-Life Examples of the Uniform Distribution


The uniform distribution is a a probability distribution in which every value between an interval from a to b is equally likely to occur.

In this article we share 5 examples of the uniform distribution in real life.

Example 1: Guessing a Birthday

If you walked up to a random person on the street, the probability that their birthday falls on a given date would follow a uniform distribution because each day of the year is equally likely to be their birthday.

For example, there are 365 days in a year so the probability that their birthday is on January 1st would be 1/365.

Similarly, the probability that their birthday is on January 2nd is 1/365.

Similarly, the probability that their birthday is on January 3rd is 1/365.

And so on.

Example 2: Rolling a Die

If you roll a die one time, the probability that it falls on a number between 1 and 6 follows a uniform distribution because each number is equally likely to occur.

For example, there are 6 possible numbers the die can land on so the probability that you roll a 1 is 1/6.

Similarly, the probability that you roll a 2 is 1/6.

Similarly, the probability that you roll a 3 is 1/6.

And so on.

Example 3: Raffle Tickets 

Suppose a basketball stadium holds a raffle in which it will randomly select one seat number out of 10,000 possible seats in the stadium and give the patron in that seat number a prize. The probability that any individual seat is chosen follows a uniform distribution.

For example, if there are 10,000 total seats then the probability that seat “1” will be chosen is 1/10,000.

Similarly, the probability that seat “2” is chosen is 1/10,000.

Similarly, the probability that seat “3” is chosen is 1/10,000.

And so on.

Example 4: Deck of Cards

Suppose you randomly select a card from a deck. The probability that the card will be either a spade, heart, club, or diamond follows a uniform distribution because each suit is equally likely to be chosen.

For example, the probability that you choose a spade is 1/4.

Similarly, the probability that you choose a heart is 1/4

Similarly, the probability that you choose a club is 1/4

Similarly, the probability that you choose a diamond is 1/4

Example 5: Spinning a Spinner

Suppose a spinner is split into three equal parts with the following colors painted on different parts: red, green, and blue. If you spin the spinner one time, the probability that it will land on any given color follows a uniform distribution because the spinner is equally likely to land on each color.

For example, the probability that the spinner lands on red is 1/3.

Similarly, the probability that the spinner lands on green is 1/3.

Similarly, the probability that the spinner lands on blue is 1/3.

Additional Resources

The following articles share examples of how other probability distributions are used in the real world:

6 Real-Life Examples of the Normal Distribution
5 Real-Life Examples of the Binomial Distribution
5 Real-Life Examples of the Poisson Distribution
5 Real-Life Examples of the Geometric Distribution

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