Exam 4: Basic Probability

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 a freshman?

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars.The probability that the residents do not own 2 cars if annual household income is not over $50,000 is:

If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain.It is an ethical practice to explain to the clienteles what the meaning of probability is.

There are only 4 empty rooms available in a student dormitory for eleven new freshmen.All the rooms are considered as homogenous so that it does not matter who is being assigned to which room.How many different ways can those 4 empty rooms be filled one student per room?

If two events are collectively exhaustive, what is the probability that both occur at the same time?

An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men.How many different ways can this team of 5 be formed?

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%.Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars.The probability that the residents of a household do not own 2 cars and have an income over $50,000 a year is:

SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken.Of 200 respondents selected, 75 were children and 125 were adults.120 preferred hamburger and 80 preferred chicken.55 of the children preferred hamburger. -Referring to Scenario 4-3, assume we know the person is a child.The probability that this individual prefers hamburger is .

A company has 2 machines that produce widgets.An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets.In addition, the new machine produces 3 times as many widgets as the older machine does.Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine?

If two events are collectively exhaustive, what is the probability that one or the other occurs?

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 black and had not claimed bias?

SCENARIO 4-2 An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm.The following result was obtained. Did Well on Midterm Did Poorly on Midterm Studying for Exam 80 20 Went Bar Hopping 30 70 -Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of exceptionally high gain.It is an unethical practice to tell the clienteles the probability of a loss in her recommendations.

A debate team of 4 is to be chosen from a class of 35.There are two twin brothers in the class.How many possible ways can the team be formed which will include only one of the twin brothers?

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 who prefers soda is _.

If either A or B must occur they are called mutually exclusive.

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 no increase in house sales in the next6 months are

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, given alcohol was involved, what proportion of accidents involved a single vehicle?

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 is selected at random, the probability that it will be properly sealed is .