Exam 4: Basic Probability

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\text { Number of Vehicles Involved }$ Did alcohol playa role? 1 2 3 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?

TABLE 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Payoff 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 Table 4-7, if you have a winning ticket, the probability that you win at least $100.00 is_____ .

Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(Aor B) = ____.

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?

TABLE 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 Table 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?

TABLE 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 Table 4-5, if a package selected at random came from Machine A, the probability that it is improperly sealed is_____ .

TABLE 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Payoff 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 Table 4-7, the probability that you win at least $100.00 is_____ .

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

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 Poorlyon Midterm Studyingror Exam 80 20 Went Bar Hopping 30 70 -Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm?

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?

$\text { TABLE 4-6 }$ 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 Table 4-6, if a randomly selected student has passed the ELM, the probability the student is from out-of-state is ____.

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

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

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 and prefers chicken is_____ .

$\text { TABLE 4-8 }$ 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 Table 4-8, what is the probability that a randomly selected student is a junior who does not live in a dormitory?

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?

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that annual household income is over $25,000 if the residents of a household own 2 cars?

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 or is white and has claimed bias?

The collection of all possible events is called

TABLE 4-4 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer. -Referring to Table 4-4, the probability a randomly selected patron is a female who prefers beer is____ .