# 4: Probability and Counting

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Probability theory is concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.

• 4.1: Sample Spaces and Probability
The mathematical theory of statistics is easier to learn when you know the language. This module presents important terms that will be used throughout the text.
• 4.2: Independent and Mutually Exclusive Events
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, with selecting each member with the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutu
• 4.3: The Addition and Multiplication Rules of Probability
The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are not independent. The events A and B are mutually exclusive events when they have no common outcomes.
• 4.4: Counting Rules
• 4.5: Probability And Counting Rules
• 4.E: Probability Topics (Optional Exercises)
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.