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 1 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%
