9: Probability
- Page ID
- 201177
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In this chapter, you will learn to:
- Write sample spaces.
- Determine whether two events are mutually exclusive.
- Use the Addition Rule.
- Calculate probabilities using both tree diagrams and combinations.
- Do problems involving conditional probability.
- Determine whether two events are independent.
- 9.1: Sample Spaces and Probability
- Probability measures the likelihood of something happening. This section defines exactly how we can measure "likelihood" mathematically, and presents a number of examples of doing so.
- 9.2: Mutually Exclusive Events and the Addition Rule
- Because events are sets, we can construct them using the union, intersection, and complement set operations. The probabilities of such "compound" events are related to the probabilities of the events from which we constructed them, but not always in the most obvious ways. This section begins the study of compound probabilities by examining unions and complements of events.
- 9.3: Probability Using Tree Diagrams and Combinations
- Finding the number of outcomes in an event, and the total number in a sample space, involves counting. Thus probability problems often have counting problems hidden within them, and the counting techniques we developed earlier in this book become handy. This section explores applications of such counting techniques as tree diagrams and combinations to probability.
- 9.4: Conditional Probability
- The probability of an event sometimes depends on whether another event also happens. So-called "conditional probability" allows us to describe and calculate probabilities in the presence of such relationships. This section defines conditional probability, related notations, and formulas for calculating it.
- 9.5: Independent Events
- Intuitively, saying that two events are "independent" should mean that neither affects the probability of the other. This section gives a mathematical meaning to this intuition and explores its consequences.
- 9.6: Bayes' Formula
- Conditional probability is helpful in real-world settings where we observe some event, A, happening, and want to know the probability of event B following. Surprisingly often though, we want to reverse this order: we observe event B, and want to know the probability that A preceded it. This section introduces Bayes' Formula, a handy tool for solving exactly this sort of problem.