Lecture 2 Flashcards
Experiment
an experiment is a process that generates well-defined outcomes.
Sample space (S)
collection of all possible outcomes
sample point
an experimental outcome is called a sample point or an element
event
an event is a set consisting of a specific collection of sample points
Complement event “formula”
The complement of an event E is defined as E roof = S\E. You can think about this as: E roof= S - E
intersection
outcomes in both event a and b
A bridge B
union
outcomes in either events A or B or both
A U B
mutually exclusive events
if two events does not occur simultaneously
Probability of an event (formula)
P(A) = n(A)/n(S)
The probability of any event is A bounded between 0 and 1
0<P(A)< 1 (och lika med)
The probability of the Complement of any event A is
P(Aroof) = P(S) - P(A) = 1-P(A)
The probability that event A, B, or both occurs is calculated as
P(AUB) = P(A) + P(B) - P(AbridgeB)
write A bridge B does not contain sample points
A bridge B = 0/
the intersection of two mutually exclusive events, A and B, has probability 0 “formula”
P(A bridge B) = 0
Probability of an event - Conditional probability
The probability of an event given that another event occurred is called conditional probability.
The original sample space is revised to account for the “new” information, i.e. certain outcomes are eliminated.
Look in notes how denoted
Probability of an event - Bayes’ theorem
determines conditional probability
independent events
P(A|B) = P(A) or P(B|A)=P(B)
–>
P (A bridge B) = P(A)P(B)
Are independent events and mutually exclusive events the same thing?
No.
Mutually exclusive; P (A bridge B) = 0 always
Independent: P (A bridge B) = P(A)P(B)
Combinations
Arrangements without respect to order
Permutations
Arrangements with respect to order
