Page 44 - Applied Statistics And Probability For Engineers

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2-2 INTERPRETATIONS OF PROBABILITY 27

resistance. Determine the number of disks in A ¨ B, A¿, and Describe each of the following events:
A ´ . B (a) A¿ (b) B¿
2-27. Samples of a cast aluminum part are classified on the (c) A ¨ B (d) A ´ B
basis of surface finish (in microinches) and edge finish. The 2-30. A sample of two items is selected without replace-
results of 100 parts are summarized as follows: ment from a batch. Describe the (ordered) sample space for
each of the following batches:
edge finish (a) The batch contains the items {a, b, c, d}.
excellent good (b) The batch contains the items {a, b, c, d, e, f, g}.
(c) The batch contains 4 defective items and 20 good items.
surface excellent 80 2
(d) The batch contains 1 defective item and 20 good items.
finish good 10 8
2-31. A sample of two printed circuit boards is selected
without replacement from a batch. Describe the (ordered)
(a) Let A denote the event that a sample has excellent surface
sample space for each of the following batches:
finish, and let B denote the event that a sample has excel-
(a) The batch contains 90 boards that are not defective, 8
lent edge finish. Determine the number of samples in
boards with minor defects, and 2 boards with major
A¿¨ B, B¿, and A ´ B .
defects.
(b) Assume that each of two samples is to be classified on the
(b) The batch contains 90 boards that are not defective, 8
basis of surface finish, either excellent or good, edge finish,
boards with minor defects, and 1 board with major
either excellent or good. Use a tree diagram to represent the
defects.
possible outcomes of this experiment.
2-32. Counts of the Web pages provided by each of two
2-28. Samples of emissions from three suppliers are classi-
computer servers in a selected hour of the day are recorded.
fied for conformance to air-quality specifications. The results
Let A denote the event that at least 10 pages are provided by
from 100 samples are summarized as follows:
server 1 and let B denote the event that at least 20 pages are
provided by server 2.
conforms
(a) Describe the sample space for the numbers of pages for
yes no
two servers graphically.
1 22 8
Show each of the following events on the sample space graph:
supplier 2 25 5 (b) A (c) B
3 30 10 (d) A ¨ B (e) A ´ B
2-33. The rise time of a reactor is measured in minutes
Let A denote the event that a sample is from supplier 1, and let
(and fractions of minutes). Let the sample space for the rise
B denote the event that a sample conforms to specifications.
time of each batch be positive, real numbers. Consider
Determine the number of samples in A¿¨ B, B¿, and A ´ B .
the rise times of two batches. Let A denote the event that the
2-29. The rise time of a reactor is measured in minutes (and rise time of batch 1 is less than 72.5 minutes, and let B
fractions of minutes). Let the sample space be positive, real denote the event that the rise time of batch 2 is greater than
numbers. Define the events A and B as follows: 52.5 minutes.
Describe the sample space for the rise time of two batches
A 5x ƒ x 72.56 graphically and show each of the following events on a two-
dimensional plot:
and (a) A (b) B¿
(c) A ¨ B (d) A ´ B
B 5x ƒ x 52.56
2-2 INTERPRETATIONS OF PROBABILITY

2-2.1 Introduction

In this chapter, we introduce probability for discrete sample spaces—those with only a finite
(or countably infinite) set of outcomes. The restriction to these sample spaces enables us to
simplify the concepts and the presentation without excessive mathematics.