3.3 Addition Rule

    Intuitively - Consider deck of cards :

                Find P(Heart or Spade) vs P(Heart or Jack)
 
 

Compound Event

    Union of 2 or more simple Events

     P(A or B) = P(A occurs or B occurs or BOTH occur)   ... inclusive or

 
Homicide Robbery Assault TOTALS
Stranger 12 379 727 1118
Acquaintance or Relative 39 106 642 787
Unknown 18 20 57 95
TOTALS 69 505 1426 2000
 
Example 1
 

Probability Assaulted or Robbed    (Mutually Exclusive sets)

        P(A or R) = 

     P(Aor R) = P(A) + P(R)
 
 Example 2                             (NOT Mutually Exclusive Sets)

Probability Robbed or Victimize by a Stranger

      P(R or S) =
 
 
 
 

        P(R or S) = P(R) + P(S) - P(R and S)
 

Addition Rule

          P(A or B) = P(A) + P(B)  -  P(A and B)
 

      IF A and B are Mutually Exclusive then P(A or B) = P(A) + P(B)
            because P(A and B) = 0
 

Test Mutually Exclusive   #2
 
 

*Flow Chart top of pg 137
 

VENN Diagrams
 
 
 
 
 

#10
 

 

#12
 

 

#16
 
 
 

Probability birthday in August or September   vs
 
 

Probability birthday is 15th or in September
 
 
 
 
 
 
 
 
Complementary Events 

 
 Probability of at Least 1 boy in family of 4 kids
 
 P(At Least 1 boy) = 1 -  P(No boys)   = 
 

#4
 
 

#6
 
 

#18
 
 

#20
 
 

#22
 

 If    and     and 
 
 

        Find P(A or B),