denoted by A∩B=∅. In this case, the sets Aand Bare said to be mutually exclusive
events or disjoint events. The notation A⊂Bis used to denote ”all elements of A
are contained in the set B” This can also be expressed B ⊃A, which is read ” B
contains A”. If the sample space contains n-sets {A 1 , A 2 ,... , A n}, then the union of
these sets is denoted
A 1 ∪A 2 ∪···∪ An or ∪n
j=1
Aj
The intersection of these sets is denoted
A 1 ∩A 2 ∩···∩ An or ∩n
j=1
Aj
If Aj∩Ak=∅, for all values of jand k, with k=j, then the sets {A 1 , A 2 ,... , A n}are
said to represent mutually exclusive events.
Probability Fundamentals
Assuming that there are hways an event can happen and f ways for the event
to fail and these ways are all equally likely to happen , then the probability pthat an
event will happen in a given trial is
p= h
h+f
(11 .17)
and the probability qthat the event will fail is given by
q= f
h+f
(11 .18)
These probabilities satisfy p+q= 1.
In general, given a finite sample space S ={e 1 , e 2 ,... , en} containing nsimple
events e 1 ,... , en, assign to each element of Sa number P(ei),i= 1 ,... , n called the
probability assigned to event eiof S. The probability numbers P(ei)assigned must
satisfy the following conditions.
1. Each probability is a nonnegative number satisfying 0 ≤P(ei)≤ 1
2. The sum of the probabilities assigned to all simple events of the sample space
must sum to unity or
∑n
j=1
P(ej) = P(e 1 ) + P(e 2 ) + ···+P(en) = 1
