Chapter 4 -BA
What is the probability of rolling a value higher than eight with a pair of fair dice
10/36 Set up sample spaces: 36 total; 10 have combination adding to more than 8.
Probability distribution
A probability model describing a random variable
Union (U)
Elementary events that belong to either A or B or both Either one whole circle even the enclosed area or both circles plus the middle where they intersect written as A U B
Two events are independent if the probability of one event is influenced by whether or not the other event occurs
False Independence of events means there is no influence.
If P(A) > 0 and P(B) > 0 and events A and B are independent, then ____________.
P(A|B) = P(A)
Complement
The Complemt (A bar) of an event A is the set of all sample space outcomes not in A P(A bar) = 1-P(A)
conditional probability of A given B
The probability of an event A, given that the event B has occurred P(AIB) P(AIB)= P(A U B)/P(B) P(B)≠0
Interpretation
if B occurred, then what is the chance of A occurring
discrete random variable
when the possible values of a random variable can be counted or listed Binomial Distribution Poisson Distribution
sample space
the set of all possible experimental outcomes
If E is an experimental outcome
then P(E) denotes the probability that E will occur and Conditions: 0 < P(E) < 1 such that: If E can never occur, then P(E) = 0 If E is certain to occur, then P(E) = 1 The probabilities of all the experimental outcomes must sum to 1
Subjective method
Assessment based on experience, expertise or intuition
The Multiplication Rule
The joint probability that A and B (the intersection of A and B) will occur P(A∩B) = P(A) • P(B|A) = P(B) • P(A|B) If A and B are independent, then the probability that A and B will occur is P(A∩B) = P(A) • P(B) = P(B) • P(A)
The General Multiplication Rule
There are two ways to calculate P(A U B) P(A n B)=P(A)xP(BIA) P(A n B)=P(B)xP(AIB)
If events A and B are mutually exclusive, then P(A|B) is always equal to zero.
True
Relative frequency method
Using the long run relative frequency Ex: the more we flip the coing the relative frequency of one would get closer to .5 each time
continuous random variable
When a random variable may assume any numerical value in one or more intervals on the real number line normal distribution exponential distribution
Probability model
a mathematical representation of a random phenomenon
Probability
a measure of the chance that an experimental outcome will occur when an experiment is carried out
A(n) ____________ is the probability that one event will occur given that we know that another event already has occurred.
conditional probability
Intersection (n)
elementary events that belong to both A and B (the middle of a ven diagram where the circle enclose each other) written as A n B
Random variable
a variable whose value is numeric and is determined by the outcome of an experiment
The set of all possible outcomes for an experiment is called a(n) ____________.
sample space
mutually exclusive
A and B are mutually exclsive if they have no sample space outcomes in common P(A n B) =0
The __________ of event X consists of all sample space outcomes that do not correspond to the occurrence of event X.
Complement
Classical method
For equally likely outcomes Ex: Tossing a Coin
Addition Rule of Probability
If A and B are mutually exclusive, then the probability that A or B will occur is P(A U B)= P(A) +P(B) If A and B are not mutually exclusive: P(A U B)= P(A) + P(B) -P(A n B)
P(A υ B) = P(A) + P(B) − P(A∩B) represents the formula for the ____________.
addition rule