Exam 4: Introduction to Probability

Students who live on campus and purchase a meal plan are randomly assigned to one of three dining halls: the Commons, Northeast, and Frazier. What is the probability that the next student to purchase a meal plan will be assigned to the Commons?

If the probability of one event occurring is .40 and the probability of a second event occurring is 0.60, then the probability that both events will occur must be 1.0 since that is the maximum value a probability can be.

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.

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical probability assessment for computing probability is used, the probability that the next customer will purchase a computer is:

Based on weather data collected in Racine, Wisconsin, on Christmas Day, the weather had the following distribution: Supposing next Christmas is dry, determine the probability that it will also be cloudy.

Two football teams play in the Super Bowl. The event of team A winning and the event of team B winning can be said to be mutually exclusive.

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. A randomly chosen driver gets lost on a road trip. Determine the probability that the driver is a woman and stops to ask for directions.

A dam on a river that holds back a water reservoir begins to leak. Engineers say that there is a 10 percent chance of the dam breaking if repairs are not made. This is an example of classical probability.

A special roulette wheel, which has an equal number of red and black spots, has come up red four times in a row. Assuming that the roulette wheel is fair, what concept allows a player to know that the probability the next spin of the wheel will come up black is 0.5?

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?)

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 two customers to enter the bank are males and go to the Loan Officer is 0.42.

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 lose both contracts?

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.

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.

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. Compute the probability that a randomly selected employee will be a female with an account balance between $100,000 and $150,000.

Sometime it is necessary to assign probabilities based on a person's belief that an outcome will occur.

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. What is the probability that she matched the paint brand?

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

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. What is the probability of the Hubble Construction Company winning the bid?

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: