Exam 4: Basic Probability

If two events are independent, what is the probability that they both occur?

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). 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%?

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

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

The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. After evaluating all the information available on the company's fundamentals and the economic environment, an analyst has determined that the probability that tomorrow's closing price will be higher than today's is determined to be 25%. This is an example of using which of the following probability approach?

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?

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 is late to the test, what is the probability that he rode his bike?

Simple probability is also called

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 or went bar hopping the weekend before the midterm?

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, given that multiple vehicles were involved, what proportion of accidents involved alcohol?

If P(A and B) = 0, then A and B must be mutually exclusive.

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

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 own 2 cars and have an income over $50,000 a year is

Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P(A and B) = ________.

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 4-11 A sample of 300 adults is selected. The contingency table below shows their registration status and their preferred source of information on current events. -Referring to Table 4-11, if an adult is selected at random, what is the probability that he/she prefer to get his/her current information from the Internet?

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 is late to the test, what is the probability that he took the bus?

TABLE 4-7 The next state lottery will have the following -Referring to Table 4-7, the probability that you win any money is ________.

TABLE 4-4 Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda. 70% said that they preferred water. 60% of the patrons were male. 80% of the males preferred water. -Referring to Table 4-4, the probability a randomly selected patron is a female who prefers water 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, determine whether the class status of a student and whether the student lives in a dormitory are independent.