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26 CHAPTER 2 PROBABILITY

2-19. Three events are shown on the Venn diagram in the (f) 1A ´ C2¿ (g) A ¨ B ¨ C
following figure: (h) B¿¨ C (i) A ´ 1B ¨ C2
2-22. In an injection-molding operation, the length and
width, denoted as X and Y, respectively, of each molded part
are evaluated. Let

A B A denote the event of 48 X 52 centimeters
B denote the event of 9 Y 11 centimeters
C denote the event that a critical length meets customer
requirements.
C
Construct a Venn diagram that includes these events. Shade
the areas that represent the following:
(a) A (b) A ¨ B
(c) A¿´ B (d) A ´ B
(e) If these events were mutually exclusive, how successful
Reproduce the figure and shade the region that corresponds to would this production operation be? Would the process
each of the following events. produce parts with X 50 centimeters and Y 10
(a) A¿ (b) A ¨ B centimeters?
(c) 1A ¨ B2 ´ C (d) 1B ´ C2¿
(e) 1A ¨ B2¿´ C 2-23. Four bits are transmitted over a digital communica-
2-20. Three events are shown on the Venn diagram in the tions channel. Each bit is either distorted or received without
following figure: distortion. Let A i denote the event that the ith bit is distorted,
i 1, p , 4 .
(a) Describe the sample space for this experiment.
(b) Are the A i ’s mutually exclusive?
Describe the outcomes in each of the following events:
A B
(c) A 1 (d) A 1 ¿
(e) A 1 ¨ A 2 ¨ A 3 ¨ A 4 (f) 1A 1 ¨ A 2 2 ´ 1A 3 ¨ A 4 2
2-24. A sample of three calculators is selected from a manu-
facturing line, and each calculator is classified as either defective
or acceptable. Let A, B, and C denote the events that the first,
second, and third calculators respectively, are defective.
(a) Describe the sample space for this experiment with a tree
C diagram.
Use the tree diagram to describe each of the following
events:
(b) A (c) B
(d) A ¨ B (e) B ´ C
Reproduce the figure and shade the region that corresponds to
2-25. A wireless garage door opener has a code determined
each of the following events.
by the up or down setting of 12 switches. How many out-
(a) A¿ (b) 1A ¨ B2 ´ 1A ¨ B¿2
comes are in the sample space of possible codes?
(c) 1A ¨ B2 ´ C (d) 1B ´ C2¿
2-26. Disks of polycarbonate plastic from a supplier are an-
(e) 1A ¨ B2¿´ C
alyzed for scratch and shock resistance. The results from 100
2-21. A digital scale is used that provides weights to the
disks are summarized below:
nearest gram.
(a) What is the sample space for this experiment? shock resistance
Let A denote the event that a weight exceeds 11 grams, let B
high low
denote the event that a weight is less than or equal to 15
grams, and let C denote the event that a weight is greater than scratch high 70 9
or equal to 8 grams and less than 12 grams. resistance low 16 5
Describe the following events.
(b) A ´ B (c) A ¨ B Let A denote the event that a disk has high shock resistance,
(d) A¿ (e) A ´ B ´ C and let B denote the event that a disk has high scratch