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The uniform distribution is a probability distribution in which all outcomes are equally likely. Examples of the uniform distribution include rolling a fair die, flipping a fair coin, randomly selecting an individual from a large population, selecting a card from a standard deck of playing cards, and drawing a number from a box containing tickets numbered from 1 to 10.
The is 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 “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.
The following articles share examples of how other probability distributions are used in the real world: