AP Statistics – Chapter 5 Notes: Probability: What are the Chances? Page 1 of 3
AP Statistics Chapter 5 – Probability: What are the Chances?
5.1: Randomness, Probability and Simulation
Probability
The probability of any outcome of a chance process is a number between 0 and 1 that describes
the proportion of times the outcome would occur in a very long series of repetitions.
Simulation
The imitation of chance behavior, based on a model that accurately reflects the situation, is
called a simulation.
Performing of a Simulation – The 4-Step Process
1. State: Ask a question of interest about some chance process.
2. Plan: Describe how to use a chance device to imitate one repetition of the process. Tell
what you will record at the end of each repetition.
3. Do: Perform many repetitions of the simulation.
4. Conclude: Use the results of your simulation to answer the question of interest.
5.2: Probability Rules
Sample Space
The sample space S of a chance process is the set of all possible outcomes.
Probability Models
Descriptions of chance behavior contain two parts:
A probability model is a description of some chance process that consists of two parts:
• a sample space S and
• a probability for each outcome.
For example: When a fair 6-sided die is rolled, the Sample Space is S = {1, 2, 3, ,4,5, 6}.
The probability for a fair die would include the probabilities of these outcomes, which are all the
same.
Outcome
1
2
3
4
5
6
Probability
1/6
1/6
1/6
1/6
1/6
1/6
Event
An event is any collection of outcomes from some chance process. That is, an event is a subset
of the sample space. Events are usually designated by capital letters, like A, B, C, and so on.
For example: For the probability model above we might define event A = die roll is odd. The
elements of the sample space S that fits this event are {1, 3, 5}. The probability of the event A,
written as P(A) is the 3/6 or ½. So we would write P(A) = 0.5, in decimal form.
