Probability Distributions: Learn It 1

  • Understand the concept of a probability distribution and its role in describing the behavior of a random variable.
  • Describe the characteristics of probability distributions.

Probability Model/Distribution

probability model/distribution

A probability model includes all possible outcomes of a chance experiment and the probabilities associated with those outcomes.

 

A probability model is also known as a probability distribution.

Notice the following important facts about probability distributions:

  • The outcomes are random events. 
  • All outcomes are assigned a probability.
  • The probabilities are numbers between [latex]0[/latex] and [latex]1[/latex]. This makes sense because each probability is a relative frequency.
  • The sum of all of the probabilities is [latex]1[/latex]. This makes sense because we have listed all the outcomes. Since each probability is a relative frequency, these outcomes make up 100% of the observations.
Imagine a fair spinner with three equally-sized sections: One section is red, one section is blue, and one section is yellow. If we spin the spinner, all three outcomes are equally likely, so the probability of each outcome is one-third.

The following table and graph display the probability model.

Outcome

Probability
Red [latex]\dfrac{1}{3}[/latex]
Yellow [latex]\dfrac{1}{3}[/latex]
Blue [latex]\dfrac{1}{3}[/latex]

A bar graph showing the percentage of time the spinner landed on each color. The bar graph represents the data above.

In this case, we can call this probability distribution a uniform probability distribution.

In a uniform probability model, each possible outcome has equal probability.