Download Chapter 2: Data

The Practice of Statistics – Chapter 6 Part 2
Chapter 6: Probability Rules!
The General Addition Rule:
P  A  B 
Special Case: if A and B are mutually exclusive (disjoint), then P  A  B  
The General Multiplication Rule:
P  A  B 
Special Case: if A and B are independent, then P  A  B  
Conditional Probability:
From the General Multiplication Rule, we can derive the formula for conditional probability (note that
P(A) cannot equal 0 since we know that A has occurred):
P  A | B 
P( B | A)  __________
Special Case: if A and B are independent, then P  A | B  
and P  B | A 
If the outcome of one event does not influence the probability of the other event, we say the two events
are ____________________. If two events have no outcomes in common (they cannot occur
simultaneously), we say the two events are ____________________ or ____________________
____________________. Disjoint events are ____________________ independent.
0.1
A
0.2
B
0.3
0.4
P  A 
P  B 
P  A  B 
P  A  B 
P  A | B 
P  B | A 
Are events A and B mutually exclusive? How can you tell?
Are events A and B independent? How can you tell?
The Practice of Statistics – Chapter 6 Part 2
Chapter 6: Probability Rules! (KEY)
The General Addition Rule:
P  A  B   P(A) + P(B) – P(A  B)
Special Case: if A and B are mutually exclusive (disjoint), then P  A  B   P(A) + P(B)
The General Multiplication Rule:
P  A  B   P(A)· P(B/A) = P(B) · P(A/B)
Special Case: if A and B are independent, then P  A  B   P(A)· P(B)
Conditional Probability:
From the General Multiplication Rule, we can derive the formula for conditional probability (note that
P(A) cannot equal 0 since we know that A has occurred):
P( A  B)
P( B)
P( B  A)
P( B | A) 
P( A)
P( A | B) 
Special Case: if A and B are independent, then P( A | B)  P( A) and P( B | A)  P( B)
If the outcome of one event does not influence the probability of the other event, we say the two events
are independent . If two events have no outcomes in common (they cannot occur simultaneously),
we say the two events are disjoint or mutually exclusive . Disjoint events are never independent.
0.1
A
0.2
B
0.3
0.4
P  A | B 
3/7
P  B | A 
.6
P  A 
.5
P  B 
.7
P  A  B   .9
P  A  B   .3
Are events A and B mutually exclusive? How can you tell?
common (not disjoint), i.e. P(A  B) = 0.3 ≠ 0.
Are events A and B independent? How can you tell?
No, because they have points in
No, since P(A|B) ≠ P(A) or P(B|A) ≠ P(B).