Chapter 4 Flashcards
Probability
Success / Total possible outcomes
Event
Any collection of results or outcomes of a procedure (birth 2f 1m)
Simple Event
An outcome or an event that can’t be further broken down (birth fmm, mff…)
Sample space
All possible simple events; all outcomes that can’t be broken down further.
P(A)
Probability A WILL occur
P(Ā)
Probability A WILL NOT occur
Relative frequency approximation of probability
P(A)= # times A occurred/ # times the procedure was repeated
Classical Probability
n different simple events with equal chance of occurring, the event A can occur in s of these n ways. s/n Exact problems
When to use relative vs classical probability
Classical approach requires equal likely outcomes. If no, use relative.
Odds in favor of A
P(A) / P(Ā) a fraction divided by a fraction b:a
Odds against A
P(Ā) / P(A) a fraction divided by a fraction a:b
P(A)+P(Ā)=?
1
P(A) impossible =?
0
P(A) certain =?
1
The complement of A?
Ā
Addition rule
P(A or B)= [P(A)+P(B)-P(A&B)]/total # outcomes
Compound event
Two or more simple events
P (AUB)
P A or B
P(AΠB)
P A and B
Multiplication rule for without replacement
P(A) & P(B)=P(A)*P(AlB)
P(BlA)
P B will happen given A already happened.
P(AlB)
P A will happen given B already happened
Multiplication rule: tx dependent as independent
If sample size is < or equal to 5% of the population
(P of A)^#trials
Multiplication rule for independent events (with replacement)
P(A&B)=P(A)*P(B)
Probability of at least one
P(at least one)=1-P(none)
At most none!
Conditional probability
P of some event when some other event has already occurred
Conditional probability equation
P(BlA)= P(A&B)/P(A) <-given
Conditional probability shortcut
smaller#/bigger# *works only when denominator is same
Opposite of none is
At least one
Fundamental counting
event A can happen n # of ways and so forth
Factorial (!)
n! denotes # possible arrangements
Permutation Rule
nPr=n!/(n-r)! ORDER MATTERS
n=#items r=#selected (s replacement)
(permutation, arrangement, sequence)
Combination Rule
nCr=n!/r!(n-r)! ORDER DOESN’T MATTER
Permutation with identical items rule
n!/n1!n2!n3!…
