This preview shows pages 1–2. Sign up to view the full content.
Chapter 7: Probability
P(A)= Probability event A occurs
P(A
c
)= represents the "probability that the complement of event A occurs"
Ex.
3 political party affiliations: Republican, Democrat, and Independent
P(A) = probability of being an Independent, P(Independent)
P(A
c
) = of "not being an Independent", P(Republican or Democrat).
Two conditions for Valid Probabilities
1.) each probability between 0 & 1
(must be between 0<=
P
<= 1)
2.) probability for all possible outcomes of a random circumstance is equal to 1 (total over all events must =1)
General Probability Rules
Rule 1
:
probability of an impossible event is zero; probability of a certain event is one.
Therefore, for any event A, the range of possible probabilities is: 0 = P(A) = 1
Rule 2:
P(S) = 1
*S =sample space of all possibilities T
he sum of all the probabilities for
all possible events is equal to one
.
Ex.
(referring to political parties) P(R)+ P(D) +P(I) = 1
Rule 3:
P(A
c
) = 1  P(A). It follows then that P(A) = 1  P(A
c
)
Rule 4 (Addition Rule):
This is the probability that
either one or both
a. mutually exclusive
 that is A & B have no outcomes in common  then P(A or B) = P(A) + P(B)
b. NOT
mutually exclusive
, then P(A or B) = P(A) + P(B)  P(A and B)
Rule 5 (Multiplication Rule):
This is the probability that
both
events occur
a.
P(A and B) = P(A)*P(BA) or P(B)*P(AB) Note: 
This symbols means "conditional" or "given".
Ex. P(AB) means the probability that event A occurs
given
event B has occurred.
b.
If A and B are
independent
 neither event influences or affects the probability that the other event occurs –
then P(A and B) = P(A)*P(B).
This particular rule extends to more than two independent events.
Ex. P(A and B and C) = P(A)*P(B)*P(C)
Rule 6 (Conditional Probability):
P(AB) =
or P(BA) =
Personal (Subjective ) probability: degree at which a given individual believes that the event will happen
ex. "What is the probability that you will leave school before you graduate?"
Relative frequency probability: the proportion of times the outcome will occur over the long run
ex. 1000 students majoring in humanities 660 were female. 66% (660/1000) chance a humanities major being female
Sample space: collection of unique, nonoverlapping possible outcomes of a random circumstance
Simple Event: one outcome in the sample space (possible outcome of a random circumstance)
Event: collection of one or more simple events in the sample space.
Complement: 2 events that do not contain any of the same simple events and together they cover entire sample space (A
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 BARROSO,JOAOR
 Statistics, Probability

Click to edit the document details