Basic Probability Flashcards
3 approaches to assessing probability
a priori
Empirical
Subjective
a priori
Classical probability. Based on prior knowledge
Empirical
Classical probability. Based on observed data
Subjective
Subjective probability. Based on individual judgment or opinion about the probability of occurrence
Probability
a numerical value that represents the chance, likelihood, possibility that an event will occur (always between 0 and 1)
Event
each possible outcome of a variable
Simple event
An outcome from a sample space with one characteristic
e.g. planned to purchase TV
Complement of an event
All outcomes that are not part of event A
e.g. did not plan to purchase TV
Joint event
Involves two or more characteristics simultaneously
e.g. planned to purchase a TV and did actually purchase TV
The sample space
The sample space is the collection of ALL possible events
For example:
all 6 faces of a dice
all 52 playing cards
Mutually exclusive events
Events that cannot occur together. Example:
Event A = Male
Event B = Female
Events A and B are mutually exclusive
Collectively exhaustive events
One of the events must occur. The set of events covers the entire sample space
e.g. member of loyalty program or not member of loyalty program
Probability rules
The probability of any event must be between 0 and 1, inclusively. 0 ≤ P(A) ≤ 1 For any event A
The sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1.
P(A) + P(B) = 1
If A and B are mutually exclusive and collectively exhaustive
The probability of a joint event, A and B:
P(A and B) = number of outcomes satisfying A and B/ total number of elementary outcomes
Computing a marginal (or simple) probability
P(A) = P(A and B1) + P(A and B2) + … + P(A and Bk)
where B1, B2, …, Bk are k mutually exclusive and collectively exhaustive events
