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Probability
by David Warwick
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Probability

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Types of Events

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simple event

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mutually exclusive events

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independent events

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dependent events

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complementary event

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Interpretations of Probability

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relative frequency

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personal probability

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coherent probabilities

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Key Definitions

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random circumstance

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sample space

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

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tree diagram

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event

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complement

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Probability Rules

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Rule 1: "not the event"

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Rule 2: addition rule for "either or"

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Rule 3: multiplication rule for "and"

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Rule 4: conditional probability

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

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Sample with replacement

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Sample without replacement

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range from 0 to 5

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

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

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

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

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

opposite events

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

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

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

one in which the outcome is unpredictable

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

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

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

any collection of one or more possible outcomes

opposite

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

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

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

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

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

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

a sample in which individuals are not eligible for subsequent selection