Page 66 - Applied statistics and probability for engineers

44 Chapter 2/Probability

(e) If the selected part has excellent surface inish, what is the (b) That there is evidence of electrical failure given that there
probability that the length is excellent? was a gas leak
(f) If the selected part has good length, what is the probability (c) That there is evidence of a gas leak given that there is
that the surface inish is excellent? evidence of electrical failure
2-103. The following table summarizes the analysis of sam- 2-107. A lot of 100 semiconductor chips contains 20 that
ples of galvanized steel for coating weight and surface roughness: are defective. Two are selected randomly, without replacement,
from the lot.
Coating Weight
(a) What is the probability that the irst one selected is
High Low
defective?
Surface High 12 16 (b) What is the probability that the second one selected is
Roughness Low 88 34 defective given that the irst one was defective?
(c) What is the probability that both are defective?
(a) If the coating weight of a sample is high, what is the
(d) How does the answer to part (b) change if chips selected
probability that the surface roughness is high?
were replaced prior to the next selection?
(b) If the surface roughness of a sample is high, what is the
2-108. A batch of 500 containers for frozen orange juice
probability that the coating weight is high?
contains 5 that are defective. Two are selected, at random, with-
(c) If the surface roughness of a sample is low, what is the
out replacement from the batch.
probability that the coating weight is low?
(a) What is the probability that the second one selected is
2-104. Consider the data on wafer contamination and location
defective given that the irst one was defective?
in the sputtering tool shown in Table 2-2. Assume that one wafer
(b) What is the probability that both are defective?
is selected at random from this set. Let A denote the event that a
(c) What is the probability that both are acceptable?
wafer contains four or more particles, and let B denote the event
Three containers are selected, at random, without replace-
that a wafer is from the center of the sputtering tool. Determine:
ment, from the batch.
| (
(a) P A ( ) (b) P A B) (d) What is the probability that the third one selected is defective
(c) P B ( ) (d) P B A| ( ) given that the irst and second ones selected were defective?
(
(
(e) P A∩ B) (f) P A∪ B) (e) What is the probability that the third one selected is defective
given that the irst one selected was defective and the second
2-105. The following table summarizes the number of
one selected was okay?
deceased beetles under autolysis (the destruction of a cell after
(f) What is the probability that all three are defective?
its death by the action of its own enzymes) and putrefaction
2-109. A batch of 350 samples of rejuvenated mitochondria
(decomposition of organic matter, especially protein, by micro-
contains 8 that are mutated (or defective). Two are selected
organisms, resulting in production of foul-smelling matter):
from the batch, at random, without replacement.
Autolysis (a) What is the probability that the second one selected is
High Low defective given that the irst one was defective?
Putrefaction High 14 59 (b) What is the probability that both are defective?
Low 18 9 (c) What is the probability that both are acceptable?
2-110. A computer system uses passwords that are exactly
(a) If the autolysis of a sample is high, what is the probability that
seven characters and each character is one of the 26 letters (a–z)
the putrefaction is low?
or 10 integers (0–9). You maintain a password for this computer
(b) If the putrefaction of a sample is high, what is the probability
system. Let A denote the subset of passwords that begin with
that the autolysis is high?
a vowel (either a, e, i, o, or u) and let B denote the subset of
(c) If the putrefaction of a sample is low, what is the probability
passwords that end with an even number (either 0, 2, 4, 6, or 8).
that the autolysis is low?
(a) Suppose a hacker selects a password at random. What is the
2-106. A maintenance irm has gathered the following
probability that your password is selected?
information regarding the failure mechanisms for air condi-
(b) Suppose a hacker knows that your password is in event A
tioning systems:
and selects a password at random from this subset. What
Evidence of Gas Leaks is the probability that your password is selected?
(c) Suppose a hacker knows that your password is in A and B
Yes No
and selects a password at random from this subset. What is
Evidence of Yes 55 17 the probability that your password is selected?
| (
electrical failure No 32 3 2-111. If P A B) = 1, must A = B? Draw a Venn diagram to
The units without evidence of gas leaks or electrical failure explain your answer.
showed other types of failure. If this is a representative sample 2-112. Suppose A and B are mutually exclusive events.
of AC failure, ind the probability Construct a Venn diagram that contains the three events A B, ,
(a) That failure involves a gas leak and C such that P A C| ( ) = 1 and P B C| ( ) = 0.