Exam 4: Basic Probability

SCENARIO 4-5 In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output.In total, 4% of the packages are improperly sealed.Also, 3% of the packages are from Machine A and are improperly sealed. -Referring to Scenario 4-5, if a package selected at random came from Machine B, the probability that it is properly sealed is .

The employees of a company were surveyed on questions regarding their educational background(college degree or no college degree) and marital status (single or married).Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates.The probability that an employee of the company does not have a college degree is:

If A and B cannot occur at the same time they are called mutually exclusive.

SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races.Given that a worker was white, the probability that the worker had claimed bias was 30%.Given that a worker was black, the probability that the worker had claimed bias was 40%.Given that a worker was other race, the probability that the worker had claimed bias was 0%. -Referring to Scenario 4-10, what is the probability that a randomly selected worker is not black and had not claimed bias?

SCENARIO 4-4 Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda.70% said that they preferred water.60% of the patrons were male.80% of the males preferred water. -Referring to Scenario 4-4, suppose a randomly selected patron prefers water.Then the probability the patron is a male is .

Twelve students in a Business Statistics class are to be formed into three teams of four.How many different ways can this be done?

There are only 4 empty rooms available in a student dormitory for eleven new freshmen.Each room is considered unique so that it matters who is being assigned to which room.How many different ways can those 4 empty rooms be filled one student per room?

If either event A or event B must occur, then events A and B are said to be

SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers.A study was recently done that emphasized the problem we all face with drinking and driving.Four hundred accidents that occurred on a Saturday night were analyzed.Two items noted were the number of vehicles involved and whether alcohol played a role in the accident.The numbers are shown below: Number of Vehicles Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Scenario 4-1, what proportion of accidents involved alcohol and a single vehicle?

If either A or B must occur they are called collectively exhaustive.

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price.Based on the closing price of the stock collected over the last month, 25% of the days the closing price was higher than previous day's closing price, 45% was lower than previous day's and 30% was the same as previous day's.Based on this information, the probability that tomorrow's closing price will be higher than today's is 25%.This is an example of using which of the following probability approach?

SCENARIO 4-8 According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior.Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20%. -Referring to Scenario 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is not a freshman?

The probability that house sales will increase in the next 6 months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be0.74.The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89.The events increase in house sales and increase in interest rates in the next 6 months are

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Pavoff Probability \ 2.00 0.0500 \ 25.00 0.0100 \ 100.00 0.0050 \ 500.00 0.0010 \ 5,000.00 0.0005 \ 10,000.00 0.0001 You buy a single ticket. -Referring to Scenario 4-7, the probability that you win at least $100.00 is .

SCENARIO 4-11 A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events. Preferred source of information Television Newspapers Radio Internet Voting registration status Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter?

SCENARIO 4-9 A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages.For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members. -Referring to Scenario 4-9, is the size of the company independent of whether stock options are offered to their board members and why?

SCENARIO 4-11 A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events. Preferred source of information Television Newspapers Radio Internet Voting registration status Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Scenario 4-11, if a randomly selected adult is a registered voter, what is the probability that he/she prefers to get his/her current information from the newspapers?

The employees of a company were surveyed on questions regarding their educational background(college degree or no college degree) and marital status (single or married).Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates.The probability that an employee of the company is married and has a college degree is:

SCENARIO 4-4 Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda.70% said that they preferred water.60% of the patrons were male.80% of the males preferred water. -Referring to Scenario 4-4, the probability a randomly selected patron is a female is _.

To ethically advertise a school lottery scheme to try to raise money for the athletic department, the organizer of the lottery does not need to explicitly specify the probability of each of the prize in the lottery.