Exam 4: Basic Probability

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

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 be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will increase but interest rates will not increase during the next 6 months 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. -Referring to Table 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are

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 not passed the ELM, the probability the student is from southern Texas is ________.

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% were 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

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

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 ________.

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?

TABLE 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 noncash 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 Table 4-9, if a company is selected at random, what is the probability that the company is small to mid-sized or offers stock options to their board members?

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. -Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also went bar hopping the weekend before the midterm?

Simple probability is also called

The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept within budget or the campaign will increase sales is ________.

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 is improperly sealed, the probability that it came from machine A is ________.

All the events in the sample space that are not part of the specified event are called

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: -Referring to Table 4-1, what proportion of accidents involved alcohol or a single vehicle?

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 single or has a college degree 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 ________.

Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room is considered unique so that it matters who is being assigned to which room. How many different ways can those eleven freshmen be allocated?

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 does not live in the dormitory, what is the probability that the student is a junior or a senior?