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Probability by Mind Map: Probability
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Probability

a number between 0 and 1 that is assigned to a possible outcome of a random circumstance

Types of Events

simple event

one outcome in a sample space, or the possible outcome of a random circumstance

mutually exclusive events

two events which do not contain any of the same simple events, or outcomes

disjoint event

independent events

knowing that one event will occur (or has occurred) does not change the probability that the other occurs

dependent events

knowing that one event will occur (or has occurred) changes the probability that the other occurs

complementary event

opposite events

Interpretations of Probability

relative frequency

proportion of times a specific outcome would occur over the long run

personal probability

the degree to which a given individual believes that an event will happen

subjective probability

coherent probabilities

the probability of one event doesn't contradict the probability of another

Key Definitions

random circumstance

one in which the outcome is unpredictable

sample space

the collection of unique, nonoverlapping possible outcomes of a random circumstance

conditional probability of the event B, given that the event A occurs: P(A|B)

the long-run relative frequency with which event B occurs when circumstances are such that A also occurs

tree diagram

a schematic representation of the sequence of events and their probabilities, including conditional probabilities based on previous events for events that happen sequentially

event

any collection of one or more possible outcomes

complement

opposite

Probability Rules

Rule 1: "not the event"

To find the probability of A^C, the complement of A, use P(A^C) = 1-P(A)

Rule 2: addition rule for "either or"

To find the probability that either A or B or both happen

Rule 2a: general

Rule 2b: mutually exclusive events

Rule 3: multiplication rule for "and"

To find the probability that two events A and B both occur simultaneously or in a sequence

Rule 3a: general

Rule 3b: independent events

Extension of Rule 3b: more than two independent events

Rule 4: conditional probability

To find the probability that B occurs given that A has occurred: P(B|A) = P(A and B)/P(A)

Bayes Rule: finding P(A|B) using P(B|A)

P(A|B) = P(A and B) / [P(B|A)P(A) + P(B|A^C)P(A^C)]

Sample with replacement

a sample in which individuals are returned to the eligible pool for each selection

Sample without replacement

a sample in which individuals are not eligible for subsequent selection