Page 80 - Applied Statistics And Probability For Engineers

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(b) If the five chips that are placed on the board are of the S2-12. A byte is a sequence of eight bits and each bit is ei-
same type, how many different layouts are possible? ther 0 or 1.
S2-9. In the laboratory analysis of samples from a chemical (a) How many different bytes are possible?
process, five samples from the process are analyzed daily. In (b) If the first bit of a byte is a parity check, that is, the first
addition, a control sample is analyzed two times each day to byte is determined from the other seven bits, how many
check the calibration of the laboratory instruments. different bytes are possible?
(a) How many different sequences of process and control S2-13. In a chemical plant, 24 holding tanks are used for fi-
samples are possible each day? Assume that the five nal product storage. Four tanks are selected at random and
process samples are considered identical and that the two without replacement. Suppose that six of the tanks contain
control samples are considered identical. material in which the viscosity exceeds the customer require-
(b) How many different sequences of process and control sam- ments.
ples are possible if we consider the five process samples to (a) What is the probability that exactly one tank in the sample
be different and the two control samples to be identical. contains high viscosity material?
(c) For the same situation as part (b), how many sequences (b) What is the probability that at least one tank in the sample
are possible if the first test of each day must be a control contains high viscosity material?
sample? (c) In addition to the six tanks with high viscosity levels, four
S2-10. In the design of an electromechanical product, seven different tanks contain material with high impurities.
different components are to be stacked into a cylindrical cas- What is the probability that exactly one tank in the sample
ing that holds 12 components in a manner that minimizes the contains high viscosity material and exactly one tank in
impact of shocks. One end of the casing is designated as the the sample contains material with high impurities?
bottom and the other end is the top. S2-14. Plastic parts produced by an injection-molding oper-
(a) How many different designs are possible? ation are checked for conformance to specifications. Each tool
(b) If the seven components are all identical, how many dif- contains 12 cavities in which parts are produced, and these
ferent designs are possible? parts fall into a conveyor when the press opens. An inspector
(c) If the seven components consist of three of one type of chooses 3 parts from among the 12 at random. Two cavities
component and four of another type, how many different are affected by a temperature malfunction that results in parts
designs are possible? (more difficult) that do not conform to specifications.
S2-11. The design of a communication system considered (a) What is the probability that the inspector finds exactly one
the following questions: nonconforming part?
(a) How many three-digit phone prefixes that are used to rep- (b) What is the probability that the inspector finds at least one
resent a particular geographic area (such as an area code) nonconforming part?
can be created from the digits 0 through 9? S2-15. A bin of 50 parts contains five that are defective. A
(b) As in part (a), how many three-digit phone prefixes are sample of two is selected at random, without replacement.
possible that do not start with 0 or 1, but contain 0 or 1 as (a) Determine the probability that both parts in the sample are
the middle digit? defective by computing a conditional probability.
(c) How many three-digit phone prefixes are possible in (b) Determine the answer to part (a) by using the subset ap-
which no digit appears more than once in each prefix? proach that was described in this section.