Probabilities Flashcards
Event
Something that either will or will not happen. Example: “Rain” is an event
because it either will or will not rain.
Trial
The opportunity for an event to occur or not occur. Example: Each day is a trial
because each day it either will or will not rain.
Independent events
Two events are independent if the occurrence of one event does not alter the
probability of the other event occurring.
Dependent events
Two events are dependent if the occurrence of one event alters the probability of
the other event occurring.
Mutually exclusive
A set of events is mutually exclusive when more than one of the events cannot
occur together
Jointly exhaustive
A set of events is jointly exhaustive when at least one of the events must occur.
Marginal probability
The probability of a single event occurring.
Pr(A)
Complement probability
The probability of a single event not occurring.
Pr(A’) = 1 – Pr(A)
Joint probability
The probability of two or more events occurring.
Pr(A and B) = Pr(A) Pr(B) if A and B are independent events.
Pr(A and B) = Pr(A) + Pr(B) – Pr(A or B)
Disjoint probability
The probability of at least one of two or more events occurring.
Pr(A or B) = Pr(A) + Pr(B) – Pr(A and B)
Conditional probability
The probability of an event occurring given that another event has occurred.
Pr(A | B) = Pr(A and B) / Pr(B)
Unconditional probability
The probability of a conditional event occurring when we do not know whether
or not the other event has occurred.
Pr(A) = Pr(A | B) Pr(B) + Pr(A | B’) Pr(B’)
Bayes’ Theorem
A theorem used to reverse the conditionality of a probability.
Pr(B | A) = Pr(A | B) Pr(B) / Pr(A)
Combination
A set of objects. Example: A set of lottery numbers is a combination because the
numbers matter but the order of the numbers does not.
Permutation
A set of ordered objects. Example: A phone number is a permutation because
both the numbers and the order of the numbers matter.
