STAT 210: Ch 3 - Probability

conditional probability

___: the probability of A given B P(A|B)

collectively exhuastive

Given the K events E1, E2, ... Ek in the sample space S, if E1∪E2∪... ∪Ek = S, these K events are ___

independent, independent, independent

If A and B are independent, then A^(c) and B^(c) are ____, A^(c) and B are ___, and B^(c) and A are ___

disjoint (or mutually exclusive), empty set

If the events A and B have no common basic outcomes, they are called ____,and their intersection, A ∩ B, is said to be the ___.

addition rule for disjoint events

If two events are disjoint (have no outcomes in common), the probability that one or the other occurs is the sum of their individual probabilities. P (A or B) = P(A) + P(B)

statistically independent

Let A and B be 2 events. The events are said to be ___ if: P(A|B) = P(A) [if P(B) > 0] P(B|A) = P(B) [if P(A) > 0]

multiplication rule of probabilities

Let A and B be two events. The ___ is P(A and B) = P(A)P(B|A) or P(A and B) = P(B)P(A|B)

complement

Let A be an event in the sample space, S. The set of basic outcomes of a random experiment belonging to S but not to A is called the ___ of A and is denoted A^(c)

bayes' theorem

Let A1,A2,...AK be K mutually exclusive and collectively exhaustive events, and let B be some other event. The conditional probability of Ai, given B, can be expressed as _____

multiplication rule of probabilities, independent

The general rule of ___ holds whether or not A and B are ___ P(A and B) = P(A)P(B|A)

addition rule of probabilities, disjoint

The general rule of ___ holds whether or not A and B are ____ P(A or B) = P(A) + P(B) - P(A and B)

binomial coefficient

The number of ways of arranging x successes among n observations is given by the ____

complement rule

The probability that an event does not occur is 1 minus the probability that the event does occur P(A^(c)) = 1- P(A)

bivariate, bivariate probabilities

These types of problems involve 2 distinct sets of events, which we label A1, A2,...AH and B1, B2,...,BK. The events Ai and Bj are mutually exclusive and collectively exhaustive within their sets, but intersections (Ai and Bj) can occur between all events from the 2 sets. The 2 sets of events, considered jointly in this way, are called ____, and the probabilities are called _____.

multiplication rule for independent events

Two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent, P(A and B) = P(A)P(B)

probability

___ of any basic outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. is measured over the range from 0 to 1. A probability of 0 indicates that the event will not occur, and a probability of 1 indicates that the event is certain to occur.

random phenomenon (or random experiment), basic outcomes, sample space, S

a process leading to two or more possible outcomes, without knowing exactly which outcome will occur. The possible outcomes from a random phenomenon are called ___, and the set of all basic outcomes is called the ____. We use ___ to denote the sample space.

event

any subset of basic outcomes from the sample space. occurs if the random experiment results in one of its constituent basic outcomes.

P(A and B) / P(B), P(A and B) / P(A)

definition of conditional probability: P(A|B) = ? provided that P(B) >0 P (B|A) = ? provided that P(A) >0

union, both

denoted by A∪B is the set of all basic outcomes in S that belong to at least one of these two events. Hence, A∪B occurs if and only if either A or B or ____ occur.

independent

disjoint events cannot be ____

intersection

the set of all basic outcomes in S that belong to both A and B. occurs if and only if both A and B occur.