Q&A Hero

Q: The binomial experiment consists of n independent, identical trials, each of which results in either success or failure and is such that the probability of success on any trial is the same.

Q: Suppose that A1, A2, and B are events where A1 and A2 are mutually exclusive events and P(A1) = .7, P(A2) = .3, P(B‚A1) = .2, P(B,A2) = .4. Find P(A1‚B).A. 0.12B. 0.26C. 0.21D. 0.14E. 0.28

Q: Suppose that A1, A2, and B are events where A1 and A2 are mutually exclusive events and P(A1) = .7, P(A2) = .3, P(B‚A1) = .2, P(B‚A2) = .4. Find P(B).A. 0.60B. 0.26C. 0.21D. 0.14E. 0.28

Q: An ad agency is developing a campaign to promote a business opening in a new mall development. To develop an appropriate mailing list, they decide to purchase lists of credit card holders from MasterCard and American Express. Combining the lists, they find the following: 40 percent of the people on the list have only a MasterCard and 10 percent have only an American Express card. Another 20 percent hold both MasterCard and American Express. Finally, 30 percent of those on the list have neither card. Suppose a person on the list is known to have a MasterCard. What is the probability that person also has an American Express card? A. .20 B. .33 C. .18 D. .70 E. .90

Q: In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. Are the events "female/male" and "belongs to a Greek organization" independent?A. Yes, independent.B. No, not independent.

Q: In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. What is the probability that an undergraduate is in a Greek organization, given that the undergraduate is a female? A. .07 B. .55 C. .127 D. .039 E. 138

Q: In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. What is the probability that one randomly selected undergraduate will be either a female or belong to a Greek organization? A. .55 B. .73 C. .80 D. .07 E. .87

Q: In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. What percentage of the undergraduates are female and in a Greek organization? A. 55% B. 25% C. 60% D. 7% E. 15%

Q: Suppose that you believe that the probability you will get a grade of B or better in Introduction to Finance is .6 and the probability that you will get a grade of B or better in Introduction to Accounting is .5. If these events are independent, what is the probability that you will receive a grade of B or better in both courses? A. 0.300 B. 0.833 C. 0.600 D. 0.500 E. 0.800

Q: A batch of 50 parts contains 6 defects. If two parts are drawn randomly, one at a time, and tested, what is the probability that both parts are defective? A. 0.014 B. 0.012 C. 0.120 D. 0.102 E. 0.222

Q: In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person has a favorable opinion or has an unfavorable opinion A. 0.00 B. 1.00 C. 0.62 D. 0.24

Q: In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person is male and has a favorable opinion. A. 0.40 B. 0.65 C. 0.62 D. 0.55 E. 0.25

Q: In a local survey, 100 citizens indicated their opinions on a revision to a local land-use plan. Of the 62 persons giving favorable responses, 40 were males. Of the 38 giving unfavorable responses, 15 were males. If one citizen is randomly selected, find the probability that person is female or has an unfavorable opinion. A. 0.83 B. 0.17 C. 0.51 D. 0.60 E. 0.61

Q: In a study of chain saw injuries, 57 percent involved arms or hands. If three different chain saw injury cases are randomly selected, find the probability that they all involved arms or hands. A. 0.570 B. 0.190 C. 0.185 D. 0.829 E. 0.325

Q: New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. Assuming that each set of rankings is equally likely, what is the probability that owners ranked Subaru first and Honda second? A. 1/3 B. 1/6 C. 1/2 D. 5/6 E. 6/6

Q: New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. Assuming that each set of rankings is equally likely, what is the probability that owners ranked Subaru third? A. 1/3 B. 1/6 C. 1/2 D. 5/6 E. 6/6

Q: New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. Assuming that each set of rankings is equally likely, what is the probability that owners ranked Subaru first? A. 1/3 B. 1/6 C. 1/2 D. 5/6 E. 6/6

Q: New car owners were asked to evaluate their experiences in buying a new car during the past 12 months. In the survey, the owners indicated they were most satisfied with their experiences at the following three dealers (in no particular order): Subaru, Honda, and Buick. When ranking the dealers, how many outcomes are possible? A. 6 B. 9 C. 8 D. 10 E. 12

Q: A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a Democrat or a Republican. A. 0.50 B. 1.00 C. 0.813 D. 0.188 E. 0.152

Q: A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is a male Republican. A. .125 B. .500 C. .333 D. .667 E. .188

Q: A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is either a woman or a Democrat. A. .538 B. .813 C. .500 D. .438 E. .875

Q: It is very common for television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that exactly one of the three households viewed the special show? A. 0.146 B. 0.084 C. 0.438 D. 0.382 E. 0.056

Q: It is very common for television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that none of the three households viewed this special show? A. 0.236 B. 0.056 C. 0.618 D. 0.382 E. 0.127

Q: It is very common for television series to draw a large audience for special events or for cliff-hanging story lines. Suppose that on one of these occasions, the special show drew viewers from 38.2 percent of all US TV households. Suppose that three TV households are randomly selected. What is the probability that all three households viewed this special show? A. 0.382 B. 0.127 C. 0.146 D. 0.726 E. 0.056

Q: A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that none graduates? A. 0.019 B. 0.003 C. 0.614 D. 0.057 E. 0.150

Q: A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that exactly one of the three graduates? A. 0.019 B. 0.003 C. 0.614 D. 0.057 E. 0.850

Q: A report on high school graduation stated that 85 percent of high school students graduate. Suppose 3 high school students are randomly selected from different schools. What is the probability that all graduate? A. 0.85 B. 0.947 C. 0.614 D. 0.283 E. 0.003

Q: Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.Is the acceptance decision at University A independent of the acceptance decision at University B?A. YesB. No

Q: Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at one, and only one, university? A. 0.50 B. 0.10 C. 0.15 D. 0.30 E. 0.45

Q: Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted by at least one of the two universities? A. 0.25 B. 0.55 C. 0.10 D. 0.35 E. 0.40

Q: Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will not be accepted at either university? A. 0.75 B. 0.45 C. 0.90 D. 0.65 E. 0.60

Q: Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at University A and rejected at University B? A. 0.10 B. 0.85 C. 0.15 D. 0.25 E. 0.65

Q: Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at both universities? A. 0.10 B. 0.25 C. 0.65 D. 0.625 E. 0.40

Q: Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Related information is given in the table. You just purchased a dinner and found that there is no napkin in your bag. What is the probability that Jan prepared your order? A. 0.200 B. 0.004 C. 0.018 D. 0.076 E. 0.100

Q: Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Related information is given in the table. You just purchased a dinner and found that there is no napkin in your bag. What is the probability that Cheryl prepared your order? A. 0.378 B. 0.091 C. 0.083 D. 0.500 E. 0.020

Q: Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Related information is given in the table. What is the probability that there is not a napkin included for a given order? A. 0.22 B. 0.24 C. 0.053 D. 0.015 E. 0.04

Q: Four employees who work as drive-through attendants at a local fast-food restaurant are being evaluated. As part of a quality improvement initiative and employee evaluation, these workers were observed over three days. One of the statistics collected was the proportion of time the employee forgot to include a napkin in the bag. Related information is given in the table. What is the probability that Cheryl prepared your dinner and forgot to include a napkin? A. 0.20 B. 0.10 C. 0.45 D. 0.02 E. 0.30

Q: Employees of a local university have been classified according to gender and job type.Are gender and type of job statistically independent?A. YesB. No

Q: Employees of a local university have been classified according to gender and job type.Are gender and type of job mutually exclusive?A. YesB. No

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is a member of the faculty? A. 0.333 B. 0.600 C. 0.550 D. 0.400 E. 0.917

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is a member of the hourly staff, given that the employee is female? A. 0.400 B. 0.133 C. 0.160 D. 0.053 E. 0.533

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female or works as an hourly staff member? A. 0.133 B. 0.533 C. 0.667 D. 0.400 E. 0.333

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female or works as a member of the faculty? A. 0.73 B. 0.08 C. 0.33 D. 0.70 E. 0.05

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is female, given that the employee is a salaried member of the staff? A. .167 B. .500 C. .625 D. 267 E. .375

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is male and salaried staff? A. .15 B. .10 C. .38 D. .50 E. .85

Q: Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is male? A. .667 B. .367 C. .333 D. .500 E. .917

Q: If P(A∩B ) = .3 and P(A|B) = .9, find P(B). A. 0.6 B. 0.3 C. 0.5 D. 0.27 E. 0.33

Q: If P(A|B) = .2 and P(B) = .8, determine the intersection of events A and B. A. 0.20 B. 1.0 C. 0.25 D. 0.16 E. 0.60

Q: If a product is made using five individual components, and P(product meets specifications) = P(E) = .98, what is the probability of an individual component meeting specifications, assuming that this probability is the same for all five components? A. 0.98 B. 0.996 C. 0.004 D. 0.02 E. 0.904

Q: What is the probability of rolling a six with a fair die five times in a row? A. 1/6 B. 1/46,656 C. 1/7,776 D. 5/7,776

Q: If events A and B are mutually exclusive, calculate P(A|B). A. Cannot be determined. B. 0 C. 1 D. 0.50

Q: If A and B are independent events, P(A) = .2, and P(B) = .7, determine A. 0.90 B. 0.14 C. 0.76 D. 0.50 E. 0.24

Q: A letter is drawn from the alphabet of 26 letters. What is the probability that the letter drawn is a vowel? A. 5/26 B. 1/26 C. 4/26 D. 21/26

Q: What is the probability that any two people chosen at random were born on the same day of the week? A. 1/7 B. 1/49 C. 2/7 D. 2/49

Q: The probability of event A occurring given that event B has already occurred is 0.61. The probability of both events occurring is 0.5. What is the probability of event B occurring? A. 0.305 B. 0.195 C. 0.390 D. 0.820 E. 0.500

Q: An urn contains five white, three red, and four black balls. Three are drawn at random and not placed back into the urn. What is the probability that no ball is red? A. 0.7500 B. 0.0156 C. 0.2917 D. 0.4219 E. 0.3818

Q: Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer neither buys beer nor buys cigars. A. 0.98 B. 0.95 C. 0.75 D. 0.96 E. 0.50

Q: Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer buys beer. A. 0.25 B. 0.01 C. 0.04 D. 0.50 E. 0.005

Q: At a college, 70 percent of the students are women and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student has received a grade of C, what is the probability that the student is female? A. 0.45 B. 0.90 C. 0.70 D. 0.64 E. 0.50

Q: At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student has received a grade of C, what is the probability that the student is male? A. 0.05 B. 0.10 C. 0.30 D. 0.17 E. 0.50

Q: At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. If a student is male, what is the probability he is a C student? A. 0.05 B. 0.10 C. 0.30 D. 0.17 E. 0.50

Q: At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is male and not a C student? A. .45 B. .50 C. .70 D. .25 E. .05

Q: At a college, 70 percent of the students are women, and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this contingency table. What is the probability that a student is female and a C student? A. .45 B. .50 C. .70 D. .25 E. .05

Q: What is the probability of winning four games in a row, if the probability of winning each game individually is 1/2? A. 1/4 B. 1/8 C. 1/2 D. 3/16 E. 1/16

Q: A family has two children. What is the probability that both are girls, given that at least one is a girl? A. 1/8 B. 1/4 C. 1/2 D. 1/3 E. 1/6

Q: Independently, a coin is tossed, a card is drawn from a deck, and a die is thrown. What is the probability of observing a head on the coin, an ace on the card, and a five on the die? A. 0.0064 B. 0.1000 C. 0.7436 D. 0.0096 E. 0.5000

Q: A card is drawn from a standard deck. Given that a face card is drawn, what is the probability it will be a king? A. 1/3 B. 1/13 C. 4/13 D. 1/12 E. 1/4

Q: A card is drawn from a standard deck. What is the probability the card is an ace, given that it is a club? A. 1/52 B. 1/13 C. 4/13 D. 1/4

Q: A pair of dice is thrown. What is the probability that one of the faces is a 3, given that the sum of the two faces is 9? A. 1/3 B. 1/36 C. 1/6 D. 1/2 E. 1/4

Q: A machine is produced by a sequence of operations. Typically, one defective machine is produced per 1000 parts. What is the probability of two nondefective machines being produced? A. 0.000999 B. 0.001 C. 0.002 D. 0.998 E. 0.500

Q: A machine is made up of 3 components: an upper part, a middle part, and a lower part. The machine is then assembled. 5 percent of the upper parts are defective, 4 percent of the middle parts are defective, and 1 percent of the lower parts are defective. What is the probability that a machine is not defective? A. 0.1000 B. 0.9029 C. 0.8000 D. 0.0002 E. 0.7209

Q: Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card? A. 0.115 B. 0.500 C. 0.231 D. 0.462 E. 0.308

Q: Given the standard deck of cards, what is the probability of drawing a red card, given that it is a face card? A. 0.500 B. 0.115 C. 0.231 D. 0.077 E. 0.308

Q: A coin is tossed 6 times. What is the probability that at least one head occurs? A. 63/64 B. 1/64 C. 1/36 D. 5/6 E. 1/2

Q: Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that only one of the items is defective? A. 0.2250 B. 0.3000 C. 0.0250 D. 0.4000 E. 0.1500

Q: Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that the item from Container 1 is defective and the item from Container 2 is not defective? A. 0.3846 B. 0.2250 C. 0.3750 D. 0.6154 E. 0.1500

Q: Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that both items are not defective? A. 0.3750 B. 0.3846 C. 0.1500 D. 0.6154 E. 0.2000

Q: A group has 12 men and 4 women. If 3 people are selected at random from the group, what is the probability that they are all men? A. 0.4219 B. 0.5143 C. 0.3929 D. 0.0156 E. 0.0045

Q: A person is dealt 5 cards from a deck of 52 cards. What is the probability they are all clubs? A. 0.2500 B. 0.0962 C. 0.0769 D. 0.0010 E. 0.0005

Q: A lot contains 12 items, and 4 are defective. If three items are drawn at random from the lot, what is the probability they are not defective? A. 0.3333 B. 0.2545 C. 0.5000 D. 0.2963 E. 0.0370