Objective Basic Principles Probabilities of Simple Events Probabilities of Compound Events Examples
This module shows how the laws of probability are used to compute probabilities of compound and conditional events.
The Probability Laws module targets the following cognitive tasks:
| Task Skills | Concepts | |
|---|---|---|
| ProbLaw-1: | Interpret the value of |
Understand that the axioms of probability |
| ProbLaw-2: | Compute |
Understand the Complement Law of probability |
| ProbLaw-3: | Compute |
Understand conditional probabilities |
| ProbLaw-4: | Identify independent events | Understand independent events |
| ProbLaw-5: | Compute |
Understand the Multiplication Law of probability for independent events |
| ProbLaw-6: | Compute |
Understand the general Multiplication Law of probability |
| ProbLaw-7: | Identify mutually exclusive events | Understand mutually exclusive events |
| ProbLaw-8: | Compute |
Understand the Addition Law of probability for mutually exclusive events |
| ProbLaw-9: | Compute |
Understand the general Addition Law of probability |
We collect sample data to make statements about the parent population. Statements about the population, based on information in the data, are necessarily uncertain. We use probability to measure the degree of uncertainty. This module examines the basic concepts of probability.
An random experiment consists of one or more trials. Each trial results in exactly one outcome from a set of possible outcomes. An event is one or more outcomes which meet some criterion. As an example, consider the experiment of tossing a coin 10 times and observing the number of heads. Each toss is a trial and the possible outcomes for each trial are Head and Tail.
An event is denoted by E and the probability of this event is P(E). The probability of the event E can be defined according to one of several definitions of probability. The a priori definition of probability is useful in certain situations.
Example #1 demonstrates how to calculate the following probabilities involving the events A and B:
| P(A); | P(A and B); | P(A or B); | P(A | B). |