Exam 4: Introduction to Probability

Cross County Bicycles makes two mountain bike models that each come in three colors. The following table shows the production volumes for last week: What is the joint probability that a product manufactured is a YZ-99 and brown?

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 the probability that a defective window was made by the Boise plant is approximately 0.16.

In playing the game Monopoly, the probability of a player landing on Park Place would be assessed using classical probability assessment.

Classical probability assessment is likely to be the most common method of probability assessment used in business decision making.

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, if a player has a handicap that is 10 or more, the probability that he or she will use a Nike golf ball is:

If two events are mutually exclusive, it is possible for them to also be independent of each other.

The URS construction company has submitted two bids, one to build a large hotel in London and the other to build a commercial office building in New York City. The company believes it has a 40% chance of winning the hotel bid and a 25% chance of winning the office building bid. The company also believes that winning the hotel bid is independent of winning the office building bid. What is the probability the company will win both contracts?

A neighborhood has 15 houses for sale. Five of these houses were less than 10 years old and the others were 10 years or older. If one house is purchased at random from this neighborhood, the probability that it is 10 years or older is 0.66.

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, the percentage of the defective cost that should be allocated to the Reno plant is approximately 42 percent.

Suppose a player is dealt 2 cards from a standard deck of 52 playing cards. To determine the probability of having a blackjack would involve classical probability.

In a survey, respondents were asked to indicate their favorite brand of cereal (Post or Kellogg's). They were allowed only one choice. What is the probability concept that implies it is not possible for a single respondent to state both Post and Kellogg's to be the favorite cereal?

Three events occur with probabilities P(E1) = 0.35, P(E2) = 0.15, P(E3) = 0.40. If the event B occurs, the probability becomes P(E1|B) = 0.25, P(B) = 0.30. Assume that E1, E2, and E3 are independent events. Calculate P(E1 and E2 and E3).

The college basketball team at West Texas State University has 10 players; 5 are seniors, 2 are juniors, and 3 are sophomores. Two players are randomly selected to serve as captains for the next game. What is the probability that both players selected are seniors?

The results of a census of 2,500 employees of a mid-sized company with 401(k) retirement accounts are as follows: Suppose researchers are going to sample employees from the company for further study. Based on the relative frequency assessment method, what is the probability that a randomly selected employee will be a male?

If a company has the opportunity to bid on three contracts, A, B, and C, then the number of these contracts that are awarded to the company would be considered an elementary event.

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 defective disk drive being received by the computer company?

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: What is the probability that a randomly selected survey participant has a college degree and prefers the NBA?

Hubble Construction Company has submitted a bid on a state government project that is to be funded by the federal government's stimulus money in Arizona. The price of the bid was predetermined in the bid specifications. The contract is to be awarded on the basis of a blind drawing from those who have bid. Five other companies have also submitted bids. Suppose that there are two contracts to be awarded by a blind draw. What is the probability of Hubble winning both contracts? Assume sampling with replacement.

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 1000 boards selected from the lumber inventory. Based on these data, if three boards are selected at random, the probability that all three were made at sawmill A is:

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: What is the probability that a randomly selected survey participant prefers the NFL?