Exam 4: Basic Probability

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 a child and prefers chicken is_____ .

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 or senior who lives in a dormitory?

$\text { TABLE 4-9 }$ 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 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 Table 4-9, if a randomly selected company is a large company, what is the probability that it offered stock options to their board members?

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, what is the probability that the cost is not kept within budget or the campaign will not increase sales?

If either event A or event B must occur, then events A and B are said to be

The collection of all the possible events is called a sample space.

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 not black and had not claimed bias?

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

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

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, the probability that a randomly selected student has passed the ELM is______.

A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-letter code. How many different possible combinations are there for the code?

$\text { TABLE 4-5 }$ 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 is selected at random, the probability that it will be properly sealed is ______.

Twelve students in a Business Statistics class are to be formed into three teams of four. How many different ways can this be done?

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 two events "preferring" beer and being a male are statistically independent.

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

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%? Interest Rate 7.0\% 7.5\% 8.0\% 8.5\% >8.5\% Probability 0.12 0.23 0.24 0.35 0.06

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 not from northern Texas is____ .

The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. What is the probability that an employee of the company is single or has a college degree?

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 percentage of the students live in a dormitory?

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, what is the probability that neither the cost is kept within budget nor the campaign will increase sales?