In a magnetic storage device, three attempts are made to read data before an error

Each of three machined parts is classified as either above or below the target specification for the part.

Each of four transmitted bits is classified as either in error or not in error.

In the final inspection of electronic power supplies, three types of nonconformities might occur: functional, minor, or cosmetic. Power supplies that are defective are further classified as to type of nonconformity.

In the manufacturing of digital recording tape, electronic testing is used to record the number of bits in error in a 350-foot reel.

In the manufacturing of digital recording tape, each of 24 tracks is classified as containing or not containing one or more bits in error.

An ammeter that displays three digits is used to measure current in milliamperes.

A scale that displays two decimal places is used to measure material feeds in a chemical plant in tons.

The following two questions appear on an employee survey questionnaire. Each answer is chosen from the fivepoint scale 1 (never), 2, 3, 4, 5 (always). Is the corporation willing to listen to and fairly evaluate new ideas? How often are my coworkers important in my overall job performance?

The concentration of ozone to the nearest part per billion

The time until a tranaction service is requested of a computer to the nearest millisecond.

The pH reading of a water sample to the nearest tenth of a unit

The voids in a ferrite slab are classified as small, medium, or large. The number of voids in each category is measured by an optical inspection of a sample.

The time of a chemical reaction is recorded to the nearest millisecond

An order for an automobile can specify either an automatic or a standard transmission, either with or without air-conditioning, and any one of the four colors red, blue, black or white. Describe the set of possible orders for this experiment

A sampled injection-molded part could have been produced in either one of two presses and in any one of the eight cavities in each press.

An order for a computer system can specify memory of 4, 8, or 12 gigabytes, and disk storage of 200, 300, or 400 gigabytes. Describe the set of possible orders.

Calls are repeatedly placed to a busy phone line until a connect is achieved.

In a magnetic storage device, three attempts are made to read data before an error recovery procedure that repositions the magnetic head is used. The error recovery procedure attempts three repositionings before an abort message is sent to the operator. Let s denote the success of a read operation f denote the failure of a read operation F denote the failure of an error recovery procedure S denote the success of an error recovery procedure A denote an abort message sent to the operator. Describe the sample space of this experiment with a tree diagram.

Three events are shown on the Venn diagram in the following figure: Reproduce the figure and shade the region that corresponds to each of the following events.

Three events are shown on the Venn diagram in the following figure: Reproduce the figure and shade the region that corresponds to each of the following events.

A digital scale is used that provides weights to the nearest gram. (a) What is the sample space for this experiment? Let A denote the event that a weight exceeds 11 grams, let B 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 or equal to 8 grams and less than 12 grams. Describe the following events. (b) (c) (d) (e) (f) (g) (h) (i)

In an injection-molding operation, the length and width, denoted as X and Y, respectively, of each molded part are evaluated. Let 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. Construct a Venn diagram that includes these events. Shade the areas that represent the following: (a) A (b) (c) (d) (e) If these events were mutually exclusive, how successful would this production operation be? Would the process produce parts with X 50 centimeters and Y 10 centimeters?

Four bits are transmitted over a digital communications channel. Each bit is either distorted or received without distortion. Let Ai denote the event that the ith bit is distorted, . (a) Describe the sample space for this experiment. (b) Are the Ai s mutually exclusive? Describe the outcomes in each of the following events: (c) (d) (e) (f) 2-24. A sample of three calculators is selected from a manufacturing 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 diagram. Use the tree diagram to describe each of the following events:

A sample of three calculators is selected from a manufacturing 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 diagram. Use the tree diagram to describe each of the following events: (b) A (c) B

A wireless garage door opener has a code determined by the up or down setting of 12 switches. How many outcomes are in the sample space of possible codes?

Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized below: shock resistance high low scratch high 70 9 resistance low 16 5 Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch

Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 100 parts are summarized as follows: edge finish excellent good surface excellent 80 2 finish good 10 8 (a) Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish. Determine the number of samples in and . (b) Assume that each of two samples is to be classified on the basis of surface finish, either excellent or good, edge finish, either excellent or good. Use a tree diagram to represent the possible outcomes of this experiment.

Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows: conforms yes no 1 22 8 supplier 2 25 5 3 30 10 Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample conforms to specifications. Determine the number of samples in and .

The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space be positive, real numbers. Define the events A and B as follows:

A sample of two items is selected without replacement from a batch. Describe the (ordered) sample space for each of the following batches: (a) The batch contains the items {a, b, c, d}. (b) The batch contains the items {a, b, c, d, e, f, g}. (c) The batch contains 4 defective items and 20 good items. (d) The batch contains 1 defective item and 20 good items

2-31. A sample of two printed circuit boards is selected without replacement from a batch. Describe the (ordered) sample space for each of the following batches: (a) The batch contains 90 boards that are not defective, 8 boards with minor defects, and 2 boards with major defects. (b) The batch contains 90 boards that are not defective, 8 boards with minor defects, and 1 board with major defects

Counts of the Web pages provided by each of two computer servers in a selected hour of the day are recorded. Let A denote the event that at least 10 pages are provided by server 1 and let B denote the event that at least 20 pages are provided by server 2. (a) Describe the sample space for the numbers of pages for two servers graphically. Show each of the following events on the sample space graph:

The rise time of a reactor is measured in minutes (and fractions of minutes). Let the sample space for the rise time of each batch be positive, real numbers. Consider the rise times of two batches. Let A denote the event that the rise time of batch 1 is less than 72.5 minutes, and let B denote the event that the rise time of batch 2 is greater than 52.5 minutes. Describe the sample space for the rise time of two batches graphically and show each of the following events on a twodimensional plot: (a) A (b) (c) (d) A B A B