Page 33 - Schaum's Outlines - Probability, Random Variables And Random Processes

PROBABILITY [CHAP 1

(b) Let B be the event that the sum is not greater than 3. Again from Fig. 1-3, we see that
B = {(i, j): i + j 5 3) = {(I, I), (1, 21, (2, I)}
and

Now A n B is the event that two faces are the same and also that their sum is not greater than 3.
Thus,

Then by definition (1.39), we obtain

Note that the probability of the event that two faces are the same doubled from 8 to 4 with the
information given.

Alternative Solution:
There are 3 elements in B, and 1 of them belongs to A. Thus, the probability of the same event
with the information given is 5.

1.41. Two manufacturing plants produce similar parts. Plant 1 produces 1,000 parts, 100 of which are
defective. Plant 2 produces 2,000 parts, 150 of which are defective. A part is selected at random
and found to be defective. What is the probability that it came from plant 1 ?

Let B be the event that "the part selected is defective," and let A be the event that "the part selected
came from plant 1." Then A n B is the event that the item selected is defective and came from plant 1.
Since a part is selected at random, we assume equally likely events, and using Eq. (1.38), we have

Similarly, since there are 3000 parts and 250 of them are defective, we have

By Eq. (1.39), the probability that the part came from plant 1 is

Alternative Solution :
There are 250 defective parts, and 100 of these are from plant 1. Thus, the probability that the
defective part came from plant 1 is # = 0.4.

1.42. A lot of 100 semiconductor chips contains 20 that are defective. Two chips are selected at
random, without replacement, from the lot.

(a) What is the probability that the first one selected is defective?
(b) What is the probability that the second one selected is defective given that the first one was
defective?
(c) What is the probability that both are defective?