Exam 4: Basic Probability

A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new Machine produces 3 times as many widgets as the older machine does. Given that a widget was Produced by the new machine, what is the probability it is not defective?

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 married and has a college degree is:

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

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

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 white and had claimed bias?

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 any of the three countries, what is the probability that the consumer is willing to share personal information with retailers in order to receive personalized offers from retailers?

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 A, the probability that it is improperly sealed is ________.

If P(A and B) = 1, then A and B must be mutually exclusive.

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 any of the three countries, what is the probability that the consumer is from Canada who plans to spend more on holiday shopping and is willing to share personal information with retailers in order to receive personalized offers from retailers?

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 any of the three countries, what is the probability that the consumer plans to spend more on holiday shopping and is willing to share personal information with retailers in order to receive personalized offers from retailers?

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of exceptionally high gain. It is an unethical practice to tell the clienteles the probability of a loss in her recommendations.

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 and prefers chicken is __________.

You know that the probability of a randomly selected student will cheat on an exam is 1%. You also know that the probability of a randomly selected student will cheat on an exam knowing that His/her fellow classmate is cheating on the exam is also 1%. Which of the following is true about The event of "the randomly selected student cheating on an exam" and "his/her classmate is Cheating on the exam"?

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 any of the three countries, what is the probability that the consumer does not plan to spend more on holiday shopping and is willing to share personal information with retailers in order to receive personalized offers from retailers?

Simple probability is also called

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

SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities. Payoff Probability \ 2.00 0.0500 \ 25.00 0.0100 \ 100.00 0.0050 \ 500.00 0.0010 \ 5,000.00 0.0005 \ 10,000.00 0.0001 You buy a single ticket. -Referring to Scenario 4-7, if you have a winning ticket, the probability that you win at least $100.00 is ________.

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, what is the probability that a randomly selected student who went bar hopping did well on the midterm?

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

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 not a registered voter or does not prefer to get his/her current information from the internet?