What are probability concepts?
help us understand inferential statistics
probability theory is the science of uncertainty
What is sample space (S)?
the collection of all possible outcomes for an experiment or trial
What is outcome (O)?
a single observation of an experiment
What is an event?
an outcome or a set of outcomes for the experiment, that is, any subset of the sample space
What are the basic properties of probabilities?
- the probability of an event is always between 0 and 1
- the sum of probabilities of all possible outcomes or trails must be 1 (sample space has a probability of 1)
- the probability of an event that cannot occur is 0
- the probability of an event that is certain to occur is 1
What is the equal-likelihood model?
prediction based on some theoretical principle
What is probability for equally likely outcomes?
if an experiment has N possible outcomes that are equally likely
probability of an event (A):
P(A) = f/N
What are mutually exclusive events?
two or more events, such that none of them have common outcomes (no overlap)
events that are not mutually exclusive have common outcomes
What is the general addition rule?
applies to events that are not mutually exclusive
P(A or B) = P(A) + P(B) - P(A and B)
What is the special addition rule?
if event A and event B are mutually exclusive (disjoint), then the general rule simplifies to a special rule:
P(A or B) = P(A) + P(B)
What is a contingency table?
deal with bivariate, qualitive data
show frequencies of two variables at the same time
What are marginal probabilities?
the probabilities of each category occurring for each variable
What are joint probabilities?
the probabilities of combinations of categories of two variables
What is conditional probability?
the probability that event B occurs given that event A occurs, denoted P(B | A)
What is the conditional probability rule?
if A and B are any two events with P(A) > 0 then:
P(B | A) = P(A and B)/P(A)
What is the general multiplication rule?
for any two events A and B:
P(A and B) = P(A) * P(B | A)
and
P(A and B) = P(B) * P(A | B)
What is independence?
one event does not affect the probability of the other event occurring
What is the special multiplication rule for two independent events?
if A and B are independent events, then,
P(A and B) = P(A) * P(B)
How are being independence and mutually exclusive (disjoint) related?
if two events are independent –> cannot be disjoint
if two events are joint –> may or may not be independent
if two events are dependent –> may or may not be disjoint
What are tree diagrams?
multiplication rules can be used to calculate the probability of each event
The multiplication rule says that P(A and B) = P(A) x P(B). What must be true about events A and B for this rule to apply?
The events must be independent
The addition rule says that P(A or B) = P(A) + P(B) What must be true about events A and B for this rule to apply?
The events must be disjoint and mutually exclusive
What are the formulas for the complement of event A?
P(A^C)
1 - P(A occurs)
P(A does not occur)
