Exam 4: Basic Probability

SCENARIO 4-6 At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM. -Referring to Scenario 4-6, the probability that a randomly selected student is not from southern Texas and has not passed the ELM 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, given that 3 vehicles were involved, what proportion of accidents involved alcohol?

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 an adult and prefers chicken is __________.

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, assume we know the person is a child. The probability that this individual prefers hamburger is __________.

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 offered stock options to their board members?

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 an adult is __________.

A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for The business venture, what is the chance that the business venture will be considered Highly Disappointing?

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?

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 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 4-1 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, given that alcohol was not involved, what proportion of the accidents were multiple vehicle?

If P(A or B) = 1.0, then A and B must be collectively exhaustive.

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

If either A or B must occur they are called collectively exhaustive.

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, is the size of the company independent of whether stock options are offered to their board members and why?

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

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 prefers soda is __________.

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

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur?

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

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 no increase in house sales in the next 6 months are