Exam 4: Introduction to Probability

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.

The Baker Oil and Gas Company has four retail locations,code-named A,B,C,and D.The following table illustrates the percentage of total company sales at each store and also the percentage of customers at that store who make purchases with debit cards: Based on this information,the probability that a customer will use a debit card is just slightly greater than 0.23.

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 have a 401(k)account balance of between $25,000 and $49,999?

A product that is produced at Ramsey Manufacturing goes through three steps to be built.At step one,the components are assembled by technicians.At step two,the product is sanded,and at step three the product is painted.The product can become defective if any of these three steps is performed incorrectly.The three steps are done by different people in different locations.We let D₁ = defect introduced at step 1,D₂ = defect introduced at step 2,and D₃ = defect introduced at step three.Based on this situation these three events would be considered to be mutually exclusive.

When a pair of dice are rolled,the outcome for each die can be said to be:

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.

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 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:

The accountant for a large U.S.company is interested in finding the probability that an account will have an incorrect balance due to being overstated or being understated.To find this probability,which probability rule is she likely to use?

The Jack In The Box franchise in Bangor,Maine,has determined that the chance a customer will order a soft drink is 0.90.The probability that a customer will order a hamburger is 0.60.The probability that a customer will order french fries is 0.50. If a customer places an order,what is the probability that the order will include a soft drink and no fries if these two events are independent?

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. )

A consumer products company is planning to introduce a new product.The method that is least likely to be used to assess the probability of the product being successful is:

In most situations,there is no difference between the events and the elementary events.

Long-time friends,Pat and Tom,agree on many things,but not the outcome of the American League pennant race and the World Series.Pat is originally from Boston,and Tom is from New York.They have a steak dinner bet on next year's race,with Pat betting on the Red Sox and Tom on the Yankees.Both are convinced they will win.What probability assessment technique is being used by the two friends?

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?

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?

Ponderosa Paint and Glass carries three brands of paint.A customer wants to buy another gallon of paint to match paint she purchased at the store previously.She can't recall the brand name and does not wish to return home to find the old can of paint.So she selects two of the three brands of paint at random and buys them. Her husband also goes to the paint store and fails to remember what brand to buy.So he also purchases two of the three brands of paint at random.Determine the probability that both the woman and her husband fail to get the correct brand of paint.(Hint: Are the husband's selections independent of his wife's selections?)

A car salesman states that the probability that the dealership sells a car on a Saturday morning is .30.The method of probability assessment that he has used is most likely classical assessment.

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

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.