Chapter 4: Probability and Probability Models

Practice flashcards covering key concepts from Chapter 4 on probability, including definitions, methods, rules, and theorems.

What defines a probability model?

A mathematical representation of a random phenomenon, including all possible values and the probabilities of those values.

What is a sample space in probability?

The set of all possible experimental outcomes from an experiment.

What are the three methods to assign probabilities to sample space outcomes?

The classical method, relative frequency method, and subjective method.

What does it mean when two events are mutually exclusive?

Two events cannot occur at the same time; their intersection is zero.

What is Bayes' Theorem used for?

To revise prior probabilities based on new evidence or information.

How is the probability of an event defined?

The sum of the probabilities of all sample space outcomes that correspond to the event.

What is conditional probability?

The probability of an event given that another event has occurred.

What is the rule of complements in probability?

The probability of the complement of event A is 1 minus the probability of A.

Explain the classical method for assigning probabilities.

Used when sample space outcomes are equally likely; each outcome is assigned a probability of 1/N.

What is the formula for calculating joint probability of two independent events?

P(A ∩ B) = P(A) • P(B).

How do you calculate the relative frequency of an event?

By dividing the number of times the event occurs by the total number of trials.

What does an event consist of in probability terms?

A set of one or more sample space outcomes.

What is the total number of experimental outcomes for k steps, each with different possible outcomes n1, n2, …, nk?

(n1)(n2)…(nk).

When using Bayes' Theorem, what does P(Si|E) represent?

The posterior probability of state Si given outcome E.

How is the probability of a union of two events calculated when they are not mutually exclusive?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

What does the term 'subjective method' refer to in probability?

Estimating probabilities based on personal judgment, expertise, or experience.