Probability Model — Definition, Formula & Examples
A probability model is a representation of a chance process that lists all possible outcomes (the sample space) and gives each outcome a probability. The probabilities must be between 0 and 1 and must add up to exactly 1.
A probability model consists of a sample space of all possible outcomes together with an assignment of probabilities to each outcome such that for every outcome and .
How It Works
To build a probability model, first identify every possible outcome of the experiment. Then assign a probability to each outcome based on theory (like equally likely outcomes) or on data from repeated trials. Check that no probability is negative and that all probabilities sum to 1. If either rule is violated, the model is not valid. A probability model can be displayed as a table, list, or diagram.
Worked Example
Problem: A bag contains 2 red marbles, 3 blue marbles, and 5 green marbles. Build a probability model for drawing one marble at random.
List the sample space: The possible outcomes by color are Red, Blue, and Green.
Assign probabilities: There are 10 marbles total. Divide each color's count by 10.
Verify the model: Each probability is between 0 and 1, and the sum equals 1.
Answer: The probability model is: P(Red) = 0.2, P(Blue) = 0.3, P(Green) = 0.5.
Why It Matters
Probability models are a core tool in Grade 7 standards (CCSS 7.SP.5–7) and form the foundation for every later probability topic. Game designers, insurance actuaries, and weather forecasters all start with a probability model before making predictions.
Common Mistakes
Mistake: Listing outcomes whose probabilities do not sum to 1.
Correction: Always add all the probabilities as a final check. If the total is not exactly 1, at least one probability is wrong or an outcome is missing.