Exam 4: Introduction to Probability

Vegetables from the summer harvest are currently being processed at Skone and Conners Foods, Inc. The manager has found a case of cans that has not been properly sealed. There are three lines that processed cans of this type, and the manager wants to know which line is most likely to be responsible for this mistake. Provide the manager this information.

The Anderson Lumber Company has three sawmills that produce boards of different lengths. The following table is a joint frequency distribution based on a random sample of 1,000 boards selected from the lumber inventory. Based on these data, the probability of selecting a board from inventory that is 10 feet long is:

An event is:

Explain what is meant by the term mutually exclusive events. Cite an example.

When a patient arrives at a clinic complaining of several specific symptoms, the doctor who makes the diagnosis says that he is 80 percent certain that the patient has a particular problem. It is likely that he is basing this assessment on relative frequency of occurrence.

Men have a reputation for not wanting to ask for directions. A Harris study conducted for Lincoln Mercury indicated that 42% of men and 61% of women would stop and ask for directions. The U.S. Census Bureau's 2012 population estimate was that for individuals 18 or over, 48.2% were men and 51.8% were women. This exercise addresses this age group. Given that a driver stops to ask for directions, determine the probability that the driver was a man.

A local FedEx/Kinkos has three black-and-white copy machines and two color copiers. Based on historical data, the chances that each black-and-white copier will be down for repairs is 0.10. The color copiers are more of a problem and are down 20% of the time each. Based on this information, what is the probability that if a customer needs a color copy, both color machines will be down for repairs?

The owners of Greg's Department Store have reason to believe that one of their employees has been stealing from the store. In an interview with the police, the owner says that she is 75 percent sure that the employee is stealing. This probability is an example of one that was assessed using classical probability.

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution: /Thompson_sn3t_WordExports/Thompson_sn3t_WordExports Based on these data, what is the probability that next Christmas will be dry?

The Crystal Window Company makes windows at three locations: Reno, Las Vegas, and Boise. Some windows made by the company contain a visible defect and must be replaced. Each defect costs the company $45.00. The Reno plant makes 40 percent of all windows while the Las Vegas and Boise plants split the remaining production evenly. A recent quality study shows that 8 percent of the Reno windows contain a defect, 11 percent of the Las Vegas windows contain a defect, while 4 percent of the windows made in Boise have a defect. Once the windows are made, they are shipped to a central warehouse where they are commingled and the location where they were made is lost. Based on this information, if a defective window is discovered, it was most likely made by the Las Vegas plant.

A car salesman has noted that the probability that the dealership sells a car on a Saturday morning is .30. Then the probability of the dealership not selling a car on Saturday morning is .70.

A distributor of outdoor yard lights has four suppliers. This past season she purchased 40% of the lights from Franklin Lighting, 30% from Wilson & Sons, 20% from Evergreen Supply, and the rest from A. L. Scott. In prior years, 3% of Franklin's lights were defective, 6% of the Wilson lights were defective, 2% of Evergreen's were defective, and 8% of the Scott lights were defective. When the lights arrive at the distributor, she puts them in inventory without identifying the supplier. Suppose that a defective light string has been pulled from inventory; what is the probability that it was supplied by Franklin Lighting?

Suppose a quality manager for Dell Computers has collected the following data on the quality status of disk drives by supplier. She inspected a total of 700 disk drives. What is the probability of a defect given that company B supplied the disk drive?

When customers come to a bank, there are three primary locations they may select to go to: teller, loan officer, or escrow department. Based on past experience, the following probability distribution applies: Seventy percent of customers are males. Thus, the probability that the next customer to enter the bank is a male who goes to the teller is 1.30.

What method of probability assessment would most likely be used to assess the probability that a major earthquake will occur in California in the next three years?

Micron Technology has sales offices located in four cities: Dallas, Seattle, Boston, and Los Angeles. An analysis of the company's accounts receivables reveals the number of overdue invoices by days, as shown here. Assume the invoices are stored and managed from a central database. If a randomly selected invoice is from the Los Angeles office, what is the probability that it is 60 or fewer days overdue?

When customers come to a bank, there are three primary locations they may select to go to: teller, loan officer, or escrow department. Based on past experience, the following probability distribution applies: Seventy percent of customers are males. The probability that the next customer will be male and will go to either the teller or the escrow department is 0.49.

Drake Marketing and Promotions has randomly surveyed 200 men who watch professional sports. The men were separated according to their educational level (college degree or not) and whether they preferred the NBA or the National Football League (NFL). The results of the survey are shown: Suppose a survey participant is randomly selected and you are told that he has a college degree. What is the probability that this man prefers the NFL?

The following probability distribution was subjectively assessed for the number of sales a salesperson would make if he or she made five sales calls in one day. Given this distribution, the probability that the number of sales is more than 2 is 0.80.

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution: Based on the data, what is the probability that next Christmas will be rainy or cloudy and dry?