Exam 4: Basic Probability

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, what is the probability that an adult who prefers to get his/her current information from the internet will be a registered voter?

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?

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 properly sealed is ________.

An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain. It is an ethical practice to explain to the clienteles what the meaning of probability is.

If event A and event B cannot occur at the same time, then events A and B are said to be

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 China, 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?

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

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 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?

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 the China or 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?

When using the general multiplication rule, P(A and B) is equal to a) $P ( A \mid B ) P ( B )$ . b) $P ( A ) P ( B )$ . c) $P ( B ) / P ( A )$ . d) $P ( A ) / P ( B )$ .

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 China, 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?

Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P(A or B) = __________.

If two events are mutually exclusive, what is the probability that both occur at the same time?

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:

SCENARIO 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 Scenario 4-4, the probability a randomly selected patron is a female who prefers soda is __________.

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:

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?

SCENARIO 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 Scenario 4-4, the probability a randomly selected patron is a female who prefers water is __________.

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 the U.S. or 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?