Download Chapter 2: Data

The Practice of Statistics – Chapter 6
Chapter 6: Probability & Simulation: The Study of Randomness
Randomness & Probability Models:
Behavior is _______________ if, while individual outcomes are uncertain, for a large number of
repetitions, outcomes are regularly distributed. A situation in which we know what outcomes could
happen, but we don’t know which particular outcomes will happen is called a _______________
_______________ .
The _______________ of an outcome is the proportion of times the outcome would occur for a large
number of repetitions (in the long run).
The set of all possible outcomes of an event is the _______________ of the event.
Probability Rules:
The probability of any event is between _______________ . A probability of _____ indicates the event
will ___________ occur, and a probability of _____ indicates the event will ___________ occur.
 P  A 
The probability that event A does not occur is one minus the probability that A does occur. That A will
not occur is called the _______________ of A and is denoted _____.
P  AC  
The _______________ of two or more events is the event that ____________________ of those events
occurs.
Addition Rule for the Union of Two Events:
A
B
P  A or B   P  A  B  
The ____________________ of two or more events is the event that all of those events occur.
Multiplication Rule for the Intersection of Two Events:
A
B
P A and B  P A  B 
The Practice of Statistics – Chapter 6
If events A and B are _______________ (they have no outcomes in common), then the probability that A
or B occurs is the probability that A occurs ________ the probability that B occurs.
P  A or B  
Events A and B are ____________________ if knowing that one occurs does not change the probability
that the other occurs.
If events A and B are ____________________ then the probability of A and B equals the probability of A
_______________ the probability of B.
P  A and B  
If events A and B are independent, then their complements, Ac and Bc are also ____________________
and Ac is ____________________ of B.
The probability that event A occurs if we know for certain that event B will occur is called
____________________ probability.
The ____________________ probability of A given B is denoted: _______________
If events A and B are ____________________ then knowing that event B will occur does not change the
probability of A so for independent events:
P  A | B 
The Practice of Statistics – Chapter 6
Chapter 6: Probability & Simulation: The Study of Randomness (Key)
Randomness & Probability Models:
Behavior is random if, while individual outcomes are uncertain, for a large number of repetitions,
outcomes are regularly distributed. A situation in which we know what outcomes could happen, but we
don’t know which particular outcomes will happen is called a random phenomenon .
The probability of an outcome is the proportion of times the outcome would occur for a large number
of repetitions (in the long run).
The set of all possible outcomes of an event is the sample space of the event.
Probability Rules:
The probability of any event is between 0 and 1 . A probability of 0 indicates the event will never
occur, and a probability of 1 indicates the event will always occur.
0 ≤ 𝑃(𝐴) ≤ 1
The probability that event A does not occur is one minus the probability that A does occur. That A will
not occur is called the complement of A and is denoted P(AC) .
P  AC   1 – P(A)
The union of two or more events is the event that __at least one____ of those events occurs.
Addition Rule for the Union of Two Events:
A
B
P A or B  P A  B  P A  PB  P A and B
The _intersection_______ of two or more events is the event that all of those events occur.
Multiplication Rule for the Intersection of Two Events:
A
B
P A and B  P A  B  P A PB | A
P  B | A 
P  B  A
P  A
The Practice of Statistics – Chapter 6
If events A and B are _disjoint or mutually exclusive_____ (they have no outcomes in common), then the
probability that A or B occurs is the probability that A occurs __plus___ the probability that B occurs.
P  A or B   P(A U B) = P(A) + P(B)
Events A and B are _independent________ if knowing that one occurs does not change the probability
that the other occurs.
If events A and B are ___independent______ then the probability of A and B equals the probability of A
____times______ the probability of B.
P  A and B   P(A) X P(B)
If events A and B are independent, then their complements, Ac and Bc are also ___independent______
and Ac is ___independent______ of B.
The probability that event A occurs if we know for certain that event B will occur is called _conditional_
probability.
The __conditional_______ probability of A given B is denoted: ___P(A|B)________
If events A and B are __independent_______ then knowing that event B will occur does not change the
probability of A so for independent events:
P  A | B   __P(A)__