Page 15 - Probability, Random Variables and Random Processes
P. 15
CHAP. 11 PROBABILITY
Thus, combining with axiom 1, we obtain
0 < P(A) 5 1
Property 5 implies that
P(A u B) I P(A) + P(B)
since P(A n B) 2 0 by axiom 1.
1.5 EQUALLY LIKELY EVENTS
A. Finite Sample Space:
Consider a finite sample space S with n finite elements
where ti's are elementary events. Let P(ci) = pi. Then
3. If A = u &, where I is a collection of subscripts, then
if1
B. Equally Likely Events:
When all elementary events (5, (i = 1,2, . . . , n) are equally likely, that is,
p1 =p2 = "*- - Pn
then from Eq. (1.35), we have
and
where n(A) is the number of outcomes belonging to event A and n is the number of sample points
in S.
1.6 CONDITIONAL PROBABILITY
A. Definition :
The conditional probability of an event A given event B, denoted by P(A I B), is defined as
where P(A n B) is the joint probability of A and B. Similarly,
