Week 3 - Probability Flashcards
What is an event?
an outcome of an experiment or survey.
What is an elementary event?
an outcome that satisfies that only one criterion.
What is a joint event?
an outcome that satisfies two or more criteria
What would be a complement of event A?
all events that are not part of an event A.
What is a random variable?
An outcome of a random trial or number.
What is probability?
a number that represents the chance that a
particular event will occur for a random variable (always between
0 and 1).
Impossible – event that has no chance
Certain - event 100% happening
What are collectively exhaustive events?
set of events that includes all the possible events
What are independent events?
two events are independent if the
occurrence of either event does not affect the probability of the other event
old mid question
What are mutually exclusive events?
a set of events that cannot occur
at the same time.
If two events are not mutually exclusive, the probability
of either event A or event B occurring is the sum of their
separate probabilities minus the probability of their
simultaneous occurrence (the joint probability).
If two events A and B are independent, what is the probability of them both happening?
the probability of both events occurring is equal to the product of their individual probabilities.
𝑷 𝑨𝑩 = 𝑷[𝑨] ∙ 𝑷[𝑩]
If two events A and B are not independent, what is the probability of them both happening?
the probability of both events A and B occurring is the product of the
probability of event A multiplied by the probability of event B occurring, given that event A has occurred.
𝑷 [𝑨𝑩] = 𝑷[𝑨] ∙ 𝑷[𝑩|𝑨]
pretty sure it was on one exam
What is a conditional probability?
A conditional probability is the probability of one event, given that another
event has occurred.
P (A|B) = P (A and B) / P(B)
old mid question
What is Bayes theorem?
Bayes Theorem, however, is concerned with some event that has already occurred and calculates the probabilities regarding how it occurred. It is applicable when two or more
events can cause another event to happen.
P (A|C) =
P (C|A) x P(A) /
( P (C|A) x P(A) + P (C|B) x P(B) )
What is the multiplicative rule?
For dependent events:
P (A and B) = P(A) * P(B|A)
P (A and B) = P(B) * P(A|B)
For independent events:
P (A and B) = P(A) * P(B)
What is the addition rule?
For dependent events:
P (A or B) = P(A) +P(B) - P(A and B)
For independent events:
P (A or B) = P(A) + P(B)
