Exam 4: Basic Probability

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 own 2 cars and have an income over $50,000 a year is:

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, if a randomly selected worker had not claimed bias, what is the probability that the worker is white?

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 that a widget was produced by the new machine, what is the probability it is not defective?

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

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, determine whether the class status of a student and whether the student lives in a dormitory are independent.

A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?).If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing?

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 and prefers to get his/her current information from the television?

If P (A and B) = 1, then A and B must be mutually exclusive.

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, set up a contingency table.

If P (A or B) = 1.0, then A and B must be mutually exclusive.

SCENARIO 4-6 At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state.All students must take and pass an Entry Level Math (ELM) test.60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM. -Referring to Scenario 4-6, the probability that a randomly selected student is someone from northern Texas who has not passed the ELM 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 not a registered voter or does not prefer to get his/her current information from the internet?

There are 47 contestants at a national dog show.How many different ways can contestants fill the first place, second place, and third place positions?

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 more than one vehicle?

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, what is the probability that a randomly selected student did well on the midterm and went bar hopping the weekend before the midterm?

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 A, the probability that it is improperly sealed 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, is the preferred source of current information independent of the voting registration status?

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 had not claimed bias?

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, what proportion of the students do not live in a dormitory?

If $\mathrm { P } ( A \text { and } B ) = 0$ , then A and B must be collectively exhaustive.