B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

8.1 Concept of Probability 397
Exam ple 8.2 Assign probabilities to the events Ae, A 0 , B, AeB, and A 0 B in Fig. 8.1.
Because Ae = ((2 U (4 U (6) where (2, (4, and (6 are mutually exclusive,
From Eq. (8.7) it follows that
1
P(Ae) = 2
(8.9a)
Similarly,
1
P(A0) = 2
P(B) =
(8.9b)
(8.9c)
From Fig. 8.1 we also observe that
and
(8.10a)
Similarly,
1
P(A 0 B) = 3
(8.10b)
We can also show that
P(S) = 1
(8.11)
This result can be proved by using the relative frequency. Let an experiment be repeated N
times (N large). Because Sis the union of all possible outcomes, S occurs in every trial. Hence,
N out of N trials lead to event S, and the result follows.
Exam ple 8.3
Two dice are thrown. Determine the probability that the sum on the dice is seven.
I
For
this experiment, the sample space contains 36 sample points because 36 possible
outcomes exist. All the outcomes are equally likely. Hence, the probability of each outcome
is 1/36.