A First Course in Quality Engineering, 2nd Edition

74 A First Course in Quality Engineering

2.5.1.3.2  The Extension of the Addition Theorem

When there are three events—A, B, and C, as shown in the sketch below—the

addition theorem becomes:

A

B

C

S

P A B C P A P B P C P A B P A C

P B C P A B C

∪ ∪

( )

=

(

)

+

(

)

+

( )

− ∩

(

)

− ∩

( )

− ∩

( )

+ ∩ ∩

( )

Similar extension can be made for four, ve, or any number of events; and the

expression on the right-hand side becomes more and more complex� When

the events are all mutually exclusive, however, the extension is simple for

any number of events: if A

1

, A

2

,…, A

k

are all mutually exclusive events, then:

P A A A P A P A P A

k k1 2 1 2

∪ ∪ ∪

( )

=

( )

+

( )

+ +

( )

 

.

2.5.1.3.3  Compleme ...