Page 49 - Applied Statistics And Probability For Engineers

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32 CHAPTER 2 PROBABILITY

2-38. A sample space contains 20 equally likely outcomes. shock resistance
If the probability of event A is 0.3, how many outcomes are in high low
event A?
scratch high 70 9
2-39. Orders for a computer are summarized by the op-
resistance low 16 5
tional features that are requested as follows:
Let A denote the event that a disk has high shock resistance,
proportion of orders
and let B denote the event that a disk has high scratch resist-
no optional features 0.3
ance. If a disk is selected at random, determine the following
one optional feature 0.5
probabilities:
more than one optional feature 0.2 (a) P1A2 (b) P1B2
(c) P1A¿2 (d) P1A ¨ B2
(a) What is the probability that an order requests at least one (e) P1A ´ B2 (f) P1A¿´ B2
optional feature?
2-46. Samples of a cast aluminum part are classified on the
(b) What is the probability that an order does not request
basis of surface finish (in microinches) and edge finish. The
more than one optional feature?
results of 100 parts are summarized as follows:
2-40. If the last digit of a weight measurement is equally
likely to be any of the digits 0 through 9, edge finish
(a) What is the probability that the last digit is 0? excellent good
(b) What is the probability that the last digit is greater than or surface excellent 80 2
equal to 5? finish good 10 8
2-41. A sample preparation for a chemical measurement is
completed correctly by 25% of the lab technicians, completed Let A denote the event that a sample has excellent surface fin-
with a minor error by 70%, and completed with a major error ish, and let B denote the event that a sample has excellent
by 5%. length. If a part is selected at random, determine the following
probabilities:
(a) If a technician is selected randomly to complete the prepa-
ration, what is the probability it is completed without (a) P1A2 (b) P1B2
error? (c) P1A¿2 (d) P1A ¨ B2
(b) What is the probability that it is completed with either a (e) P1A ´ B2 (f) P1A¿´ B2
minor or a major error? 2-47. Samples of emissions from three suppliers are classi-
fied for conformance to air-quality specifications. The results
2-42. A credit card contains 16 digits between 0 and 9.
from 100 samples are summarized as follows:
However, only 100 million numbers are valid. If a number is
entered randomly, what is the probability that it is a valid
conforms
number?
yes no
2-43. Suppose your vehicle is licensed in a state that issues
license plates that consist of three digits (between 0 and 9) fol- 1 22 8
lowed by three letters (between A and Z). If a license number supplier 2 25 5
is selected randomly, what is the probability that yours is the 3 30 10
one selected?
Let A denote the event that a sample is from supplier 1, and let
2-44. A message can follow different paths through
B denote the event that a sample conforms to specifications.
servers on a network. The senders message can go to one of
If a sample is selected at random, determine the following
five servers for the first step, each of them can send to five
probabilities:
servers at the second step, each of which can send to four
(a) P1A2 (b) P1B2
servers at the third step, and then the message goes to the re-
(c) P1A¿2 (d) P1A ¨ B2
cipients server.
(e) P1A ´ B2 (f) P1A¿´ B2
(a) How many paths are possible?
2-48. Use the axioms of probability to show the following:
(b) If all paths are equally likely, what is the probability that a
message passes through the first of four servers at the (a) For any event E, P1E¿2 1 P1E2 .
third step? (b) P1 2 0
2-45. Disks of polycarbonate plastic from a supplier are an- (c) If A is contained in B, then P1A2 P1B2
alyzed for scratch and shock resistance. The results from 100
disks are summarized as follows: