Exam 4: Basic Probability

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 and the campaign will increase sales is:

SCENARIO 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 Scenario 4-8, determine whether the class status of a student and whether the student lives in a dormitory are independent.

SCENARIO 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 Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are

SCENARIO 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 Scenario 4-11, if an adult is selected at random, what is the probability that he/she prefers to get his/her current information from the internet?

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

SCENARIO 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 Scenario 4-3, the probability that a randomly selected individual is a child or prefers hamburger is __________.

SCENARIO 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 Scenario 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 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 both house sales and interest rates will increase during The next 6 months is:

Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(B|A) = __________.

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

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

SCENARIO 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 Scenario 4-5, if a package selected at random came from Machine B, the probability that it is improperly sealed is ________.

SCENARIO 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 Scenario 4-10, what is the probability that a randomly selected worker is not black and had not claimed bias?

SCENARIO 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 Scenario 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?

SCENARIO 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 Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter who prefers to get his/her current information from the television?

SCENARIO 4-12 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. The survey also found that the percentage of consumers from the U.S., Canada, and China who said that they were willing to share personal information with retailers in order to receive personalized offers from retailers were 55%, 46% and 72%, respectively. Assume that there are equal portions of consumers being surveyed from each of the three countries, the survey results are good representations of the three populations of consumers, and whether a consumer plans to spend more on holiday shopping is statistically independent of whether he/she is willing to share personal information with retailers in order to receive personalized offers from retailers. -Referring to Scenario 4-12, if you randomly select a consumer from Canada, what is the probability that the consumer does not plan to spend more on holiday shopping and is not willing to share personal information with retailers in order to receive personalized offers from retailers?

SCENARIO 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 Scenario 4-9, if a randomly selected company offered stock options to their board members, what is the probability that it is a large company?

SCENARIO 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 Scenario 4-8, what is the probability that a randomly selected student is a junior who does not live in a dormitory?

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:

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: