Exam 4: Basic Probability

TABLE 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 Table 4-10, if a randomly selected worker had claimed bias, what is the probability that the worker is white?

TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main 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 Involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Table 4-1, given that alcohol was not involved, what proportion of the accidents were multiple vehicle?

TABLE 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 Table 4-10, what is the probability that a randomly selected worker is black and had not claimed bias?

TABLE 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 Voting registration status Television Newspapers Radio Internet Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Table 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter or prefers to get his/her current information from radio?

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

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 annual household income is over $50,000 if the residents of a household own 2 cars is

If P(A or B)= 1.0, then A and B must be collectively exhaustive.

TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main 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 Involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Table 4-1, what proportion of accidents involved alcohol or a single vehicle?

Suppose A and B are independent events where P(A)= 0.4 and P(B)= 0.5. Then P(A or B)= ________.

If P(A)= 0.4 and P(B)= 0.6, then A and B must be mutually exclusive.

TABLE 4-12 Jake woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice. -Referring to Table 4-12, if Jake is late to the test, what is the probability that he rode his bike?

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 not include any of the twin brothers?

TABLE 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 Table 4-4, the probability a randomly selected patron prefers soda is ________.

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 basis of her probability estimate is.

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

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?

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

TABLE 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 Voting registration status Television Newspapers Radio Internet Registered 45 30 45 36 Not registered 35 44 45 20 -Referring to Table 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter who prefer to get his/her current information from the television?

TABLE 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 Table 4-3, the probability that a randomly selected individual is an adult or a child is ________.

TABLE 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 Table 4-2, the events "Did Well on Midterm" and "Studying for Exam" are