Probability and statistics 7th edition solutions

If there are three machine tools, four polishing tools, and three painting tools, how many different routings consisting of machining, followed by polishing, and followed by painting for a part are possible?

New designs for a wastewater treatment tank have proposed three possible shapes, four possible sizes, three locations for input valves, and four locations for output valves. How many different product designs are possible?

A manufacturing process consists of 10 operations that can be completed in any order. How many different production sequences are possible? From equation 2. A batch of semiconductor chips is inspected by choosing a sample of 5 chips. Assume 10 of the chips do not conform to customer requirements. That is ! In a sheet metal operation, three notches and four bends are required. If the operations can be done in any order, how many different ways of completing the manufacturing are possible?

In the laboratory analysis of samples from a chemical process, five samples from the process are analyzed daily.

In addition, a control sample is analyzed twice each day to check the calibration of the laboratory instruments. Assume that the five process samples are considered identical and that the two control samples are considered identical.

In the layout of a printed circuit board for an electronic product, 12 different locations can accommodate chips. Therefore, 2. Consider the design of a communication system. In the design of an electromechanical product, 12 components are to be stacked into a cylindrical casing in a manner that minimizes the impact of shocks. One end of the casing is designated as the bottom and the other end is the top.

Therefore, 12! A bin of 50 parts contains 5 that are defective. A sample of 10 parts is selected at random, without replacement. How many samples contain at least four defective parts?

From the 5 defective parts, select 4, and the number of ways to complete this step is 5! Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 cavities in which parts are produced, and these parts fall into a conveyor when the press opens.

An inspector chooses 3 parts from among the 12 at random. Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications.

A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries. Determine the following: a P A. A part selected for testing is equally likely to have been produced on any one of six cutting tools. An injection-molded part is equally likely to be obtained from any one of the eight cavities on a mold.

A credit card contains 16 digits between 0 and 9. However, only million numbers are valid. If a number is entered randomly, what is the probability that it is a valid number?

Total possible: , but only are valid. In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states and that is usually found in the following states:.

The probability is 0. A message can follow different paths through servers on a network. Suppose your vehicle is licensed in a state that issues license plates that consist of three digits between 0 and 9 followed by three letters between A and Z.

If a license number is selected randomly, what is the probability that yours is the one selected? The results from disks are summarized as follows:. If a disk is selected at random, determine the following probabilities: a P A. Magnesium alkyls are used as homogenous catalysts in the production of linear low-density polyethylene LLDPE , which requires a finer magnesium powder to sustain a reaction.

Redox reaction experiments using four different amounts of magnesium powder are performed. Each result may or may not be further reduced in a second step using three different magnesium powder amounts. Each of these results may or may not be further reduced in a third step using three different amounts of magnesium powder. The number of experiments that complete all three steps is 9k out of 13k.

The frequency of each type of transaction in the second column can be used as the percentage of each type of transaction. The average number of selects operations required for each type of transaction is shown. Let A denote the event of transactions with an average number of selects operations of 12 or fewer. Let B denote the event of transactions with an average number of updates operations of 12 or fewer.

Calculate the following probabilities. If a sample is selected at random, determine the following probabilities: a P A. Consider the hospital emergency room data is given below. Let A denote the event that a visit is to hospital 4, and let B denote the event that a visit results in LWBS at any hospital. Let A denote the event that the patient is in the group treated with interferon alfa, and let B denote the event that the patient has a complete response. Determine the following probabilities.

A specific design is randomly generated by the Web server when you visit the site. If you visit the site five times, what is the probability that you will not see the same design? A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text.

Total number of possible designs is The sample space of all possible designs that may be seen on five visits. This space contains outcomes. The number of outcomes in which all five visits are different can be obtained as follows. On the first visit any one of designs may be seen.

On the second visit there are remaining designs. On the third visit there are remaining designs. On the fourth and fifth visits there are and remaining designs, respectively. Suppose that an operating room needs to schedule three knee, four hip, and five shoulder surgeries. Assume that all schedules are equally likely. Determine the probability for each of the following: a All hip surgeries are completed before another type of surgery.

A computer system uses passwords that contain exactly eight characters, and each character is one of 26 lowercase letters a—z or 26 uppercase letters A—Z or 10 integers 0—9. Determine the probability of each of the following: a A b B c A password contains at least 1 integer. A manufacturer of front lights for automobiles tests lamps under a high-humidity, high-temperature environment using intensity and useful life as the responses of interest. The following table shows the performance of lamps:.

Can the lamp manufacturer meet this demand? Consider the hospital emergency room data given below. Let A denote the event that a visit is to hospital 4, and let B. Strands of copper wire from a manufacturer are analyzed for strength and conductivity.

The results from strands are as follows:. Are these two events mutually exclusive? A computer system uses passwords that are six characters, and each character is one of the 26 letters a—z or 10 integers 0—9. Uppercase letters are not used. Let A denote the event that a password begins with a vowel either a, e, i, o, or u , and let B denote the event that a password ends with an even number either 0, 2, 4, 6, or 8.

Suppose a hacker selects a password at random. Determine the following probabilities: a P A. Let A denote the event that the design color is red, and let B denote the event that the font size is not the smallest one. Use the addition rules to calculate the following probabilities. A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters a—z or 26 uppercase letters A—Z or 10 integers 0—9.

Assume all passwords are equally likely. Let A and B denote the events that consist of passwords with only letters or only integers, respectively. P contains exactly 2 integers Number of positions for the integers is 8! Consider the three patient groups. The groups consisted of patients with different drug therapies such as prednisone and infliximab : sequential. Radiographs of hands and feet were used to evaluate disease progression. Suppose that a patient is selected randomly.

Let A denote the event that the patient is in group 1, and let B denote the event that there is no progression. The analysis of results from a leaf transmutation experiment turning a leaf into a petal is summarized by type of transformation completed:. Let A denote the event that a leaf completes the color transformation and let B denote the event that a leaf completes the textural transformation.

The total number of experiments is Samples of skin experiencing desquamation are analyzed for both moisture and melanin content. The results from skin samples are as follows:. Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content. The following table summarizes the number of deceased beetles under autolysis the destruction of a cell after its death by the action of its own enzymes and putrefaction decomposition of organic matter, especially protein, by microorganisms, resulting in production of foul-smelling matter :.

Let A denote the event that autolysis is high and let B denote the event that putrefaction is high. A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning systems:. The units without evidence of gas leaks or electrical failure showed other types of failure. Consider the endothermic reactions given below.

Let B denote the event that the heat absorbed is above target. A batch of containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the batch. Three containers are selected, at random, without replacement, from the batch. Suppose A and B are mutually exclusive events.

An article in The Canadian Entomologist Harcourt et al. The following table shows the number of larvae that survived at each stage of development from eggs to adults. Let A denote the event that an egg survives to an adult Let EL denote the event that an egg survives at early larvae stage Let LL denote the event that an egg survives at late larvae stage Let PP denote the event that an egg survives at pre-pupae larvae stage Let LP denote the event that an egg survives at late pupae stage a P A.

The groups consisted of patients with different drug therapies such as prednisone and infliximab : sequential monotherapy group 1 , step-up combination therapy group 2 , initial combination therapy group 3 , or initial combination therapy with infliximab group 4. Determine the following probabilities: a P B A.

Let F denote the event that a connector fails and let W denote the event that a connector is wet. The edge roughness of slit paper products increases as knife blades wear. Let R denote the event that a product exhibits surface roughness. Let N, A, and W denote the events that the blades are new, average, and worn, respectively.

A lot of semiconductor chips contains 20 that are defective. Determine the probability that the second chip selected is defective. Determine the probability that all are defective. Let A and B denote the events that the first and second chips selected are defective, respectively.

This newer method looked better, but the results changed when stone diameter was considered. Open surgery is better for both stone sizes, but less successful in total. In , E. Explain how open surgery can be better for both stone sizes but worse in total. Open surgery.

The overall success rate depends on the success rates for each stone size group, but also the probability of the groups. For open surgery, the dominant group large stone has a smaller success rate while for PN, the dominant group small stone has a larger success rate.

Let A denote the event that a visit is to hospital 4 and let B denote the event that a visit results in LWBS at any hospital. Let A denote the event that the patient is in group 1, and let B denote the event for which there is no progression.

Determine the probability that the ad color is red and the font size is not the smallest one. Let R denote red color and F denote that the font size is not the smallest. Because the Web sites are generated randomly these events are independent. Determine the following probabilities: a All hip surgeries are completed first given that all knee surgeries are last.

Alternatively, one can reason that when all knee surgeries are last, there are has all knee surgeries first. Alternatively, one can reason that when all knee surgeries are last, there are 4 hip and 5 shoulder surgeries that remain to schedule. Alternatively, one can conclude that with knee surgeries in periods 2 through 4, there are 7! Alternatively, one can conclude that with knee surgeries last, there are surgeries in the first two periods.

Therefore, A and B are not independent. A batch of containers of frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement, from the batch. Let A and B denote the events that the first and second containers selected are defective, respectively. Are events A and B independent? Redundant array of inexpensive disks RAID is a technology that uses multiple hard drives to increase the speed of data transfer and provide instant data backup.

Suppose that the probability of any hard drive failing in a day is 0. What is the probability of data loss? Assume that data loss occurs if both drives fail within the same day. Assume that data loss occurs if at least one drive fails within the same day. A test of a printed circuit board uses a random test pattern with an array of 10 bits is equally likely to be 0 or 1.

Assume the bits are independent. Let A i denote the event that the ith bit is a one. The number of 2. The probability that a lab specimen contains high levels of contamination is 0. Five samples are checked, and the samples are independent. It is useful to work one of these exercises with care to illustrate the laws of probability. Let H i denote the event that the ith sample contains high levels of contamination. Therefore, the answer is 0. Therefore, the answer is 5 0.

Assume that the results from opponents are independent and that when the player is defeated by an opponent the game ends. Eight cavities in an injection-molding tool produce plastic connectors that fall into a common stream. A sample is chosen every several minutes.

Assume that the samples are independent. Let A denote the event that a sample is produced in cavity one of the mold. The number of sequences in 8 8 1 4 7 which four out of five samples are from cavity one is 5. A credit card contains 16 digits. It also contains the month and year of expiration. Suppose there are 1 million credit card holders with unique card numbers. A hacker randomly selects a digit credit card number.

What is the probability that the hacker correctly selects the month and year of expiration? The following circuit operates if and only if there is a path of functional devices from left to right.

The probability that each device functions is as shown. Assume that the probability that a device is functional does not depend on whether or not other devices are functional. What is the probability that the circuit operates?

Let A denote the upper devices function. Let B denote the lower devices function. Are these events independent?

Are A and B independent events? Explain why or why not. Assume the probability. The integrated circuit fails to function if any gate fails. Determine the value for p so that the probability that the integrated circuit functions is 0. Solution Manual for 3rd edition have answers to chapters 2, 3, 4, 5, 6, 7, 8, 9, 10 and Cover of the main textbook is the first image. File Specification for 6th edition international student version. File Specification for Second File of 3rd edition.

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