Page 79 - Applied Statistics And Probability For Engineers

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2-4

Then, the second step is to select the remaining four parts from the 47 acceptable parts in the
bin. The second step can be completed in

47 47!
a b 178,365 different ways
4 4! 43!

Therefore, from the multiplication rule, the number of subsets of size six that contain exactly
two defective items is
3 178,365 535,095

As an additional computation, the total number of different subsets of size six is found
to be

50 50!
a b 15,890,700
6 6! 44!

When probability is discussed in this chapter, the probability of an event is determined as
the ratio of the number of outcomes in the event to the number of outcomes in the sample
space (for equally likely outcomes). Therefore, the probability that a sample contains exactly
two defective parts is

535,095
0.034
15,890,700

Note that Example S2-7 illustrates the hypergeometric distribution.

EXERCISES FOR SECTION 2-1.4
S2-1. An order for a personal digital assistant can specify can begin. Within each set of five, operations can be com-
any one of five memory sizes, any one of three types of dis- pleted in any order. How many different production se-
plays, any one of four sizes of a hard disk, and can either in- quences are possible?
clude or not include a pen tablet. How many different systems S2-6. In a sheet metal operation, three notches and four
can be ordered? bends are required. If the operations can be done in any order,
S2-2. In a manufacturing operation, a part is produced by how many different ways of completing the manufacturing are
machining, polishing, and painting. If there are three machine possible?
tools, four polishing tools, and three painting tools, how many S2-7. A lot of 140 semiconductor chips is inspected by
different routings (consisting of machining, followed by pol- choosing a sample of five chips. Assume 10 of the chips do not
ishing, and followed by painting) for a part are possible? conform to customer requirements.
S2-3. New designs for a wastewater treatment tank have (a) How many different samples are possible?
proposed three possible shapes, four possible sizes, three loca- (b) How many samples of five contain exactly one noncon-
tions for input valves, and four locations for output valves. forming chip?
How many different product designs are possible? (c) How many samples of five contain at least one noncon-
S2-4. A manufacturing process consists of 10 operations forming chip?
that can be completed in any order. How many different pro- S2-8. In the layout of a printed circuit board for an elec-
duction sequences are possible? tronic product, there are 12 different locations that can accom-
S2-5. A manufacturing operations consists of 10 opera- modate chips.
tions. However, five machining operations must be com- (a) If five different types of chips are to be placed on the
pleted before any of the remaining five assembly operations board, how many different layouts are possible?