Page 48 - Applied statistics and probability for engineers

26 Chapter 2/Probability

Then, the second step is to select the remaining 4 parts from the 47 acceptable parts in the bin. The second step can be
completed in
⎛ 47⎞ 47!
,
⎜ ⎝ 4 ⎠ ⎟ = 4 43! = 178 365 different ways
!
Therefore, from the multiplication rule, the number of subsets of size 6 that contain exactly 2 defective parts is
=
×
,
,
3 178 365 535 095
As an additional computation, the total number of different subsets of size 6 is found to be
⎛ 50⎞ 50!
,
,
⎜ ⎝ 6 ⎠ ⎟ = 6 44! = 15 890 700
!
Exercises FOR SECTION 2-1

Problem available in WileyPLUS at instructor’s discretion.
Tutoring problem available in WileyPLUS at instructor’s discretion
Provide a reasonable description of the sample space for each 2-14. An order for an automobile can specify either an automatic
of the random experiments in Exercises 2-1 to 2-17. There can or a standard transmission, either with or without air condition-
be more than one acceptable inter pretation of each experiment. ing, and with any one of the four colors red, blue, black, or white.
Describe any assumptions you make. Describe the set of possible orders for this experiment.
2-15. A sampled injection-molded part could have been pro-

2-1. Each of three machined parts is classiied as either above
duced in either one of two presses and in any one of the eight
or below the target specii cation for the part.
cavities in each press.

2-2. Each of four transmitted bits is classiied as either in error
2-16. An order for a computer system can specify memory of 4,
or not in error.
8, or 12 gigabytes and disk storage of 200, 300, or 400 gigabytes.

2-3. In the inal inspection of electronic power supplies, either
Describe the set of possible orders.
units pass, or three types of nonconformities might occur: func-
2-17. Calls are repeatedly placed to a busy phone line
tional, minor, or cosmetic. Three units are inspected.
until a connection is achieved.
2-4. The number of hits (views) is recorded at a high-volume
2-18. Three attempts are made to read data in a magnetic
Web site in a day.
storage device before an error recovery procedure that reposi-
2-5. Each of 24 Web sites is classii ed as containing or not
tions the magnetic head is used. The error recovery procedure
containing banner ads.
attempts three repositionings before an “abort’’ message is sent
2-6. An ammeter that displays three digits is used to measure
to the operator. Let
current in milliamperes.
2-7. A scale that displays two decimal places is used to meas- s denote the success of a read operation
ure material feeds in a chemical plant in tons. f denote the failure of a read operation
2-8. The following two questions appear on an employee S denote the success of an error recovery procedure
survey questionnaire. Each answer is chosen from the i ve- F denote the failure of an error recovery procedure
point scale 1 (never), 2, 3, 4, 5 (always). A denote an abort message sent to the operator
Is the corporation willing to listen to and fairly evaluate Describe the sample space of this experiment with a tree diagram.
new ideas? 2-19. Three events are shown on the Venn diagram in the fol-
How often are my coworkers important in my overall lowing i gure:
job performance?
A B
2-9. The concentration of ozone to the nearest part per
billion.
2-10. The time until a service transaction is requested of a
computer to the nearest millisecond.
2-11. The pH reading of a water sample to the nearest tenth
C
of a unit.
2-12. The voids in a ferrite slab are classii ed as small,

Reproduce the igure and shade the region that corresponds to
medium, or large. The number of voids in each category is
each of the following events.
measured by an optical inspection of a sample. (
2-13. The time of a chemical reaction is recorded to the near- (a) A′ (b) A∩ B (c) A∩ B) ∪ C
(
(
′
est millisecond. (d) B ∪ C)′ (e) A∩ B) ∪ C