Exam 4: Basic Probability

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

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 had not claimed bias?

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

If P(A and B) = 1, then A and B must be collectively exhaustive.

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

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 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. 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?

If either event A or event B must occur, 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 any of the three countries, what is the probability that the consumer plans to spend more on holiday shopping?

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 Neither the cost is kept within budget nor the campaign will increase sales 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 basis of her probability estimate is.

If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

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 China 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 4-4 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 two events "preferring water" and "preferring soda" are independent.

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 events increase in house sales and increase in interest rates in the next 6 Months are

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 neither house sales nor interest rates will increase During the next 6 months is:

SCENARIO 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: Number of Vehicles Involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Scenario 4-1, what proportion of accidents involved more than one vehicle?

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

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

SCENARIO 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: Number of Vehicles Involved Did alcohol play a role? Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 -Referring to Scenario 4-1, what proportion of accidents involved alcohol or a single vehicle?