MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If two events are mutually exclusive, what is the probability that one or the other occurs? A) 0 B) 1.00 C) 0.50 D) cannot be determined from the information given 2) If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? A) 0 B) 1.00 C) 0.50 D) cannot be determined from the information given 3) If two events are independent, what is the probability that they both occur? A) 0.50 B) 0 C) 1.00 D) cannot be determined from the information given 4) 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? A) 25% B) 20% C) 10% D) 15% 5) A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30‐year mortgage with a 10% down payment). Interest Rate 7.0% 7.5% 8.0% 8.5% > 8.5% Probability 0.12 0.23 0.24 0.35 0.06 If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 8.0%? A) 0.41 B) 0.06 C) 1.00 D) 0.59 6) 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. What is the probability that both house sales and interest rates will increase during the next 6 months? A) 0.185 B) 0.10 C) 0.705 D) 0.90 7) According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. What is the probability that the residents of a household do not own 2 cars and have an income over $25,000 a year? A) 0.48 B) 0.12 C) 0.22 D) 0.18
8) 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 a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine? A) 0.489 B) 0.15 C) 0.511 D) 0.08 TABLE 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? 1 2 3 Totals Yes 50 100 20 170 No 25 175 30 230 Totals 75 275 50 400 9) Referring to Table 4‐1, what proportion of accidents involved more than one vehicle?
A) 275/400 or 68.75% B) 325/400 or 81.25% C) 75/400 or 18.75% D) 50/400 or 12.5% 10) Referring to Table 4‐1, what proportion of accidents involved alcohol and a single vehicle?
A) 195/400 or 48.75% B) 245/400 or 61.25% C) 25/400 or 6.25% D) 50/400 or 12.5% 11) Referring to Table 4‐1, what proportion of accidents involved alcohol or a single vehicle?
A) 245/400 or 61.25% B) 195/400 or 48.75% C) 25/400 or 6.25% D) 50/400 or 12.5% 12) Referring to Table 4‐1, given that multiple vehicles were involved, what proportion of accidents involved
alcohol?
A) 120/400 or 30% B) 120/170 or 70.59% C) 120/325 or 36.92% D) 120/230 or 52.17% 13) Referring to Table 4‐1, given that 3 vehicles were involved, what proportion of accidents involved alcohol?
A) 20/170 or 11.77% B) 20/30 or 66.67% C) 20/400 or 5% D) 20/50 or 40% 14) Referring to Table 4‐1, given that alcohol was not involved, what proportion of the accidents were multiple
vehicle?
A) 50/170 or 29.41% B) 120/170 or 70.59% C) 25/230 or 10.87% D) 205/230 or 89.13% 15) A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is
selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students?
A) 0.0625 B) 1.00 C) 0.0256 D) 0.16
16) Whenever p = 0.1 and n is small, the binomial distribution will be
17) If the outcomes of a random variable follow a Poisson distribution, then their A) mean equals the standard deviation. B) median equals the variance. C) mean equals the variance. D) median equals the standard deviation. 18) A study was recently done in which 500 people were asked to indicate their preferences for one of three products. The following table shows the breakdown of the responses by gender of the respondents. Product Preference Gender A B C Male 80 20 10 Female 200 70 120 Based on these data, the probability that a person in the population will prefer product A can be assessed as: A) 0.56 B) 0.18 C) 0.286 D) 0.16 19) A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next yearʹs rat orders be, assuming this distribution does not change? A) $650 B) $520 C) $637 D) $780 20) A package delivery service claims that no more than 5 percent of all packages arrive at the address late. Assuming that the conditions for the binomial hold, if a sample of size 10 packages is randomly selected and the 5 percent rate holds, what is the probability that more than 2 packages will be delivered late? A) 0.0862 B) 0.0105 C) 0.0746 D) 0.0116 21) The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5. Based on this, the probability that 2 containers will contain a total of less than 2 defects is: A) 0.0073. B) 0.1359. C) 0.0223. D) 0.1850. 22) A small city has two taxi companies (A and B). Each taxi company has 5 taxis. A motel has told these companies that they will randomly select a taxi company when one of its customers needs a cab. This morning 3 cabs were needed, assuming that no one individual taxi can be used more than once, what is the probability that 2 of the cabs selected will be from Company A and the other will be from B? A) 0.583 B) 0.25 C) 0.5 D) 0.417 23) Thirty‐six of the staff of 80 teachers at a local intermediate school are certified in Cardio‐Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
A) 65 days B) 5 days C) 45 days D) 81 days
24) A probability distribution is an equation that
A) assigns a value to the variability in the sample space.
B) associates a particular probability of occurrence with each outcome in the sample space. C) assigns a value to the center of the sample space.
25) Which of the following about the binomial distribution is not a true statement? A) Each outcome is independent of the other. B) The random variable of interest is continuous. C) Each outcome may be classified as either ʺevent of interestʺ or ʺnot event of interest.ʺ D) The probability of event of interest must be constant from trial to trial. 26) What type of probability distribution will most likely be used to analyze the number of chocolate chip parts per cookie in the following problem? The quality control manager of Marilynʹs Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. The manager is interested in analyzing the probability that any particular cookie being inspected has fewer than 5.0 chip parts. A) Poisson distribution B) hypergeometric distribution C) binomial distribution D) none of the above
27) If event A and event B cannot occur at the same time, then events A and B are said to be A) statistically independent. B) collectively exhaustive. C) mutually exclusive. D) none of the above 28) The collection of all possible events is called A) a simple probability. B) a sample space. C) the null set. D) a joint probability. 29) The method of probability assessment that relies on an examination of historical data from similar situations is: A) historical assessment. B) subjective assessment. C) classical assessment. D) relative frequency of occurrence . 30) Harrison Water Sports has three retail outlets: Seattle, Portland, and Phoenix. The Seattle store does 50 percent of the total sales in a year, while the Portland store does 35 percent of the total sales. Further analysis indicates that of the sales in Seattle, 20 percent are in boat accessories. The percentage of boat accessories at the Portland store is 30 and the percentage is 25 at the Phoenix store. Overall, the probability that a sale by Harrison Water Sports will be for a boat accessory is: A) 0.2425. B) 0.75. C) 0.105. D) None of the above.
