Exam 4: Using Probability and Probability Distributions

One of the difficulties in using the relative frequency of occurrence method for assessing probabilities in business situations is getting a large enough set of examples that match the one in question.

A used car lot has 15 cars.Five of these cars were manufactured in the United States and the others were made in other countries.If one car is purchased at random from this car lot,the probability that it is a U.S.car is 0.33.

The method of probability assessment that relies on an examination of historical data from similar situations is:

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:

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.Overall,the probability that a sale by Harrison Water Sports will be for a boat accessory is:

If two events are independent,then

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:

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.

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

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.

If a single die is rolled (a cube where the sides are numbered 1 through 6),the probability of rolling at least a 3 is 0.33.

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

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.

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.

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 2 or 3 is 0.50.

When the salesperson makes a sale,there are three possible sales levels: large,medium,and small.The probability of a large sale is 0.20 and the chance of a medium sale is 0.60.Thus,when a sale is made,the chance of it being a small sale is 0.20.

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:

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.

Suppose a single die (a 6-sided cube with sides numbered 1 through 6)is rolled once.The event of interest is defined as rolling an even number.This can be said to be an elementary event.

Mutually exclusive means that the occurrence of event A has no effect on the probability of the occurrence of event B,and independent means the occurrence of event A prevents the occurrence of event B.