Chapter 7

The probability of an event occurring is 1 minus the probability that it doesn't occur P(A) = 1- P(A^c)

Complement rule

When the probability comes from the long-run relative frequency of the event's occurrence, it is an empirical probability.

Empirical probability

to find the probability of an event from a conditional distribution we write? and pronounce it?

P(B|A) and say "the probability of B given A"

Two events are _____ if the fact that one event occurs does not change the probability of the other. Event A and B are ______ when P(B|A) = P(B)

Independence

P(B|A) = P(A and B) / P(A) has to be greater than zero to work

conditional probability

For any two events, A and B, the probability of A or B is: P (A or B) = P(A) + P(B) - P(A and B) (Does not require disjoint events)

general addition rule

For any two events, A and B, the probability of A and B is: P(A and B) = P(A) X P(B|A)

general multiplication rule

The probability that two events both occur

joint probabilities

States that the long-run relative frequency of repeated, independent events settles down to the true relative frequency as the number of trails increases

law of large numbers

The probability of an event is is?

long-run relative frequency

In a joint probability table a marginal probability is the probability distribution of either variable separately, usually found in the rightmost column or bottom row of the table.

marginal probability

For two independent events A and B, the probability that both A and B occur is the product of the probabilities of the two events. P(A and B) = P(A) x P(B), provided that A and B are independent.

multiplication rule

when the probability is subjective and represents your personal degree of belief

personal probability

The probability of the entire sample space must be 1: P(S) = 1

probability assignment rule

The collection of all possible outcome values. The sample space has a probability of 1

sample space

When the probability comes from a mathematical model

theoretical probability

A probability is a number between 0 and 1. For any event A, ?

0 less than or equal to P(A) less than or equal to 1

If A and B are disjoint events, then the probability of A or B is P(A or B) = P(A) + P(B)

addition rule

A phenomenon consists of trials. Each trial has an outcome. Outcomes combine to make events.

:D

Two events are disjoint if they share no outcomes in common. If A and B are disjoint, then knowing that A occurs tells us that B cannot occur. Also called mutually exclusive

disjoint events