Exam 4: Basic Probability

$\text { TABLE 4-2 }$ An alcoholawareness task force at a Big-Ten universitysampled 200 studentsafter the midterm toask them whether they went barhopping the weekend before the midterm orspent the weekend studying,and whetherthey 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, what is the probability that a randomly selected student who went bar hopping will do well on the midterm?

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 B, the probability that it is improperly sealed is ______.

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 the residents of a household own 2 cars and have an income over $25,000 a year?

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 4-6, if a randomly selected student is not from southern Texas, the probability the student has not passed the ELM is _____.

At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages. How many different ways are there to order an egg, a pancake with a choice of syrup and a beverage?

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?

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 4-9 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 company is selected at random, what is the probability that the company is small to mid-sized or offered stock options to their board members?

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

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 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 is________

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

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 sophomore who does not live in a dormitory?

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?

There are only 4 empty rooms available in a student dormitory for eleven new freshmen. All the rooms are considered as homogenous so that it does not matter who is being assigned to which room. How many different ways can those 4 empty rooms be filled one student per room?

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 company is selected at random, what is the probability that the company offered stock options to their board members?

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?

If the outcome of event A is not affected by event B, then events A and B are said to be

If P(A and B) = 1, then A and B must be collectively exhaustive.

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, suppose a randomly selected patron prefers beer. Then the probability the patron is a male is _______.