Exam 4: Basic Probability

To ethically advertise a school lottery scheme to try to raise money for the athletic department, the organizer of the lottery does not need to explicitly specify the probability of each of the prize in the lottery.

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, assume we know that a person prefers chicken. The probability that this individual is an adult is ________.

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 both of the twin brothers?

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, in fact, gets to the test on time, what is the probability that he rode his bike?

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 is not from out-of-state, the probability the student has passed the ELM 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 a randomly selected adult is a registered voter, what is the probability that he/she prefers to get his/her current information from the newspapers?

The collection of all possible events is called

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 the residents of a household do not own 2 cars and have an income over $50,000 a year is

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 offered stock options to their board members, what is the probability that it is a large company?

There are only 4 empty rooms available in a student dormitory for eleven new freshmen. Each room is considered unique so that it matters 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 is small to mid-sized or offered stock options to their board members?

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?

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 4-5 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 ________.

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 and did not offer 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 events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?

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

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?

A 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). Interest Rate 4.90\% to 4.99\% 5.00\% to 5.09\% 5.10\% to 5.19\% 5.20\% to 5.29\% 5.30\% and above Probability 0.12 0.23 0.24 0.35 0.06 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 5.19%?