50 CHAPTER 2 PROBABILITYThe solution can be obtained from a partition of the graph into three columns.
The probability that there is a path of functional devices only through the three units on the
left can be determined from the independence in a manner similar to the previous example.
It isSimilarly, the probability that there is a path of functional devices only through the two units
in the middle isThe probability that there is a path of functional devices only through the one unit on the right
is simply the probability that the device functions, namely, 0.99. Therefore, with the inde-
pendence assumption used again, the solution isEXERCISES FOR SECTION 2-611 0.1^3211 0.05^221 0.99 2 0.9871 0.05^21 0.1^32-81. If and are
the events Aand Bindependent?
2-82. If and are
the events Band the complement of Aindependent?
2-83. Disks of polycarbonate plastic from a supplier are an-
alyzed for scratch and shock resistance. The results from 100
disks are summarized as follows:
shock resistance
high low
scratch high 70 9
resistance low 16 5
Let Adenote the event that a disk has high shock resistance,
and let Bdenote the event that a disk has high scratch resist-
ance. Are events Aand Bindependent?
2-84. Samples of a cast aluminum part are classified on the
basis of surface finish (in microinches) and length measure-
ments. The results of 100 parts are summarized as follows:
length
excellent good
surface excellent 80 2
finish good 10 8
Let Adenote the event that a sample has excellent surface fin-
ish, and let Bdenote the event that a sample has excellent
length. Are events Aand Bindependent?
2-85. Samples of emissions from three suppliers are classi-
fied for conformance to air-quality specifications. The results
from 100 samples are summarized as follows:conforms
yes no
122 8
supplier 2 25 5
33010Let Adenote the event that a sample is from supplier 1, and let
Bdenote the event that a sample conforms to specifications.
(a) Are events Aand Bindependent?
(b) Determine
2-86. If and Aand Bare mutually
exclusive, are they independent?
2-87. The probability that a lab specimen contains high lev-
els of contamination is 0.10. Five samples are checked, and
the samples are independent.
(a) What is the probability that none contains high levels of
contamination?
(b) What is the probability that exactly one contains high
levels of contamination?
(c) What is the probability that at least one contains high
levels of contamination?
2-88. In a test of a printed circuit board using a random test
pattern, an array of 10 bits is equally likely to be 0 or 1.
Assume the bits are independent.
(a) What is the probability that all bits are 1s?
(b) What is the probability that all bits are 0s?
(c) What is the probability that exactly five bits are 1s and five
bits are 0s?
2-89. Eight cavities in an injection-molding tool produce
plastic connectors that fall into a common stream. A sample isP 1 A 2 0.2, P 1 B 2 0.2,P 1 BƒA 2.P 1 AƒB 2 0.3, P 1 B 2 0.8, P 1 A 2 0.3,P 1 AƒB 2 0.4, P 1 B 2 0.8, P 1 A 2 0.5,c 02 .qxd 5/10/02 1:07 PM Page 50 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L:Quark Files: