Exam 4: Introduction to Probability

At a potato processing plant in the state of Washington, 400 potatoes have been examined for disease. Of these, four were diseased. Based on this, the plant manager has stated that the probability of finding a diseased potato is 0.01. He is applying subjective probability to arrive at this 0.01 value.

During the past week, of the 250 customers at the Dairy Queen who ordered a Blizzard, 50 ordered strawberry. This means that of the next five Blizzard customers, exactly one will order strawberry.

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is shown below: Based on these data, the probability that a player will use a Strata golf ball is:

If a manager were interested in assessing the probability that a new product will be successful in a New Jersey market area, she would most likely use relative frequency of occurrence as the method for assessing the probability.

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, if a board is selected that is 12 feet long, the probability that it was made at sawmill A is:

Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The Seattle store does 50 percent of the total sales in a year, while the Portland store does 35 percent of the total sales. Further analysis indicates that of the sales in Seattle, 20 percent are in boat accessories. The percentage of boat accessories at the Portland store is 30 and the percentage at the Phoenix store is 25. If a sales dollar is recorded as a boat accessory, the probability that the sale was made at the Portland store is:

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. If a customer wants both a color copy and a black-and-white copy, what is the probability that the necessary machines will be available? (Assume that the color copier can also be used to make a black- and-white copy if needed.)

The method of probability assessment that is least likely to be used by business decision makers is:

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. Calculate the probability that the driver stops to ask for directions.

When a construction company bids on a contract, the events will be win or lose. The closer the probability is to 0.50, the greater the uncertainty about whether the company will win or lose the bid.

Assume that a standard deck of 52 playing cards is randomly shuffled and the first 2 cards are dealt to you. What is the probability that you have a blackjack? A blackjack is where one card is an ace and the other card is worth 10 points. The 10-point cards are kings, queens, jacks and 10's.

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 three consecutive customers all go to a teller is approximately 0.22.

Suppose 10 students are enrolled in a class and the probability of at least 8 showing up on a given day is 90 percent. Then the probability of 7 or fewer showing that day is 10 percent.

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. What is the probability that a randomly selected invoice from the database is over 90 days old and from the Seattle office?

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 less than 2 is 0.15.

A study was recently done in which 500 people were asked to indicate their preferences for one of three products. The following table shows the breakdown of the responses by gender of the respondents. Based on these data, the probability that a person in the population will prefer product A can be assessed as:

List three methods of assessing probabilities and indicate which is least likely to be used in business decision making.

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. Based on these inspection data, what is the probability of randomly selecting a disk drive from company B?

Assume P(A) = 0.4 and P(B) = 0.2 and P(A and B) = 0.1, then the probability of P(A or B) = 0.7.

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. What is the probability that a randomly selected invoice from the database is from the Boston sales office?