Q&A Hero

Q: If two events are collectively exhaustive, what is the probability that both occur at the same time? a. 0.00 b. 0.50 c. 1.00 d. Cannot be determined from the information given.

Q: If two events are collectively exhaustive, what is the probability that one or the other occurs? a. 0.25 b. 0.50 c. 1.00 d. Cannot be determined from the information given.

Q: If A and B are mutually exclusive events with P(A) = 0.70, then P(B): a. can be any value between 0 and 1 b. can be any value between 0 and 0.70 c. cannot be larger than 0.30 d. Cannot be determined with the information given

Q: If P(A) = P(A|B), then events A and B are said to be a. mutually exclusive b. independent c. exhaustive d. complementary

Q: Which of the following statements are true? a. Probabilities must be nonnegative b. Probabilities must be less than or equal to 1 c. The sum of all probabilities for a random variable must be equal to 1 d. All of these options are true.

Q: A discrete probability distribution: a. lists all of the possible values of the random variable and their corresponding probabilities b. is a tool that can be used to incorporate uncertainty into models c. can be estimated from long-run proportions d. is the distribution of a single random variable

Q: The law of large numbers is relevant to the estimation of a. objective probabilities b. subjective probabilities c. both of these options d. neither of these options

Q: is the: a. addition rule b. commutative rule c. rule of complements d. rule of opposites

Q: The formal way to revise probabilities based on new information is to use: a. complementary probabilities b. conditional probabilities c. unilateral probabilities d. common sense probabilities

Q: A function that associates a numerical value with each possible outcome of an uncertain event is called a a. conditional variable b. random variable c. population variable d. sample variable

Q: Let A and B be the events of the FDA approving and rejecting a new drug to treat hypertension, respectively. The events A and B are: a. independent b. conditional c. unilateral d. mutually exclusive

Q: Probabilities that can be estimated from long-run relative frequencies of events are a. objective probabilities b. subjective probabilities c. complementary probabilities d. joint probabilities

Q: If events A and B are mutually exclusive, then the probability of both events occurring simultaneously is equal to a. 0.0 b. 0.5 c. 1.0 d. any value between 0.5 and 1.0

Q: The probability of an event and the probability of its complement always sum to: a. 1 b. 0 c. any value between 0 and 1 d. any positive value

Q: Probabilities that cannot be estimated from long-run relative frequencies of events are a. objective probabilities b. subjective probabilities c. complementary probabilities d. joint probabilities

Q: NARRBEGIN: SA_113_120 An oil company is planning to drill three exploratory wells in different areas of West Texas. The company estimates that each of these wells, independent of the others, has about a 30% chance of being successful. NARREND If it costs $200,000 to drill each well and a successful well will produce $1,000,000 worth of oil over its lifetime, what is the expected net value of this three-well program?

Q: NARRBEGIN: SA_113_120 An oil company is planning to drill three exploratory wells in different areas of West Texas. The company estimates that each of these wells, independent of the others, has about a 30% chance of being successful. NARREND Suppose the first well to be completed is successful. What is the probability that one of the two remaining wells is successful?

Q: NARRBEGIN: SA_113_120An oil company is planning to drill three exploratory wells in different areas of West Texas. The company estimates that each of these wells, independent of the others, has about a 30% chance of being successful.NARRENDHow many of the wells can the company expect to be successful?

Q: NARRBEGIN: SA_113_120 An oil company is planning to drill three exploratory wells in different areas of West Texas. The company estimates that each of these wells, independent of the others, has about a 30% chance of being successful. NARREND If a new pipeline will be constructed in the event that all three wells are successful, what is the probability that the pipeline will be constructed?

Q: NARRBEGIN: SA_113_120 An oil company is planning to drill three exploratory wells in different areas of West Texas. The company estimates that each of these wells, independent of the others, has about a 30% chance of being successful. NARREND What is the probability that none of the oil wells will be successful?

Q: NARRBEGIN: SA_113_120An oil company is planning to drill three exploratory wells in different areas of West Texas. The company estimates that each of these wells, independent of the others, has about a 30% chance of being successful.NARRENDFind the probability distribution of X; the number of oil wells that will be successful.

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND Are gender of patrons and drinking preference independent? Explain.

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND Suppose a randomly selected patron is a female. What is the probability that the patron prefers wine?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND Suppose a randomly selected patron is a female. What is the probability the patron prefers beer?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND Suppose a randomly selected patron prefers beer. What is the probability the patron is a male?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND Suppose a randomly selected patron prefers wine. What is the probability the patron is a male?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND What is the probability a randomly selected patron is a female who prefers beer?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND What is the probability a randomly selected patron is a female who prefers wine?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND What is the probability a randomly selected patron is a female?

Q: NARRBEGIN: SA_104_113 Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer. NARREND What is the probability a randomly selected patron prefers wine?

Q: NARRBEGIN: SA_104_113Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 60% said that they preferred beer. 70% of the patrons were male. 80% of the males preferred beer.NARRENDConstruct the joint probability table.

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND Does consumer behavior depend on the gender of consumer? Explain using probabilities.

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random enjoys or does not enjoy shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a male or a female?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a male or does not enjoy shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a female or enjoys shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a male and does not enjoy shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a female and enjoys shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a male and enjoys shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random enjoys shopping for clothing?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND What is the probability that a respondent chosen at random is a male?

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND Give an example of a joint event.

Q: NARRBEGIN: SA_91_103 A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes. NARREND Give an example of a simple event.

Q: NARRBEGIN: SA_91_103A sample of 1000 households was selected in Los Angeles to determine information concerning consumer behavior. Among the questions asked was "Do you enjoy shopping for clothing?" Of 480 males, 272 answered yes. Of 520 females, 448 answered yes.NARRENDSet up a 22 contingency table for this situation.

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDGiven that no brand 2 bats are sold on a given day, what is the probability of observing the sale of at least one brand 1 bicycle at this sporting goods store?

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDWhat is the probability of observing the sale of no more than two brand 2 bats on a given day at this sporting goods store?

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDWhat is the probability of observing the sale of at least one brand 1 bat on a given day at this sporting goods store?

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDWhat is probability of observing the sale of at least one brand 1 bat and at least one brand 2 bat on the same day at this sporting goods store?

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDDetermine the marginal probability distribution of .

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDCalculate the joint probabilities of and .

Q: NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let and be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2 = 0 = 1 = 2 = 3= 00.050.150.250.30= 10.100.250.550.57= 20.600.500.150.10= 30.250.100.050.03Marginal Distribution of 0.200.300.300.20NARRENDAreandindependent random variables? Explain why or why not.

Q: NARRBEGIN: SA_79_83Suppose that the manufacturer of a particular product assesses the joint distribution of the price per unit (P) and demand (D) for its product in the upcoming quarter as presented below. Use this information to answer the following questions. Demand (D)Price per Unit (P) 2000250030003500$200.050.050.030.150.28$250.050.060.100.050.26$300.080.100.040.030.25$350.100.050.030.030.210.280.260.200.26NARRENDWhat is the probability that the demand of this product will be less than 3500 units in the upcoming quarter, given that its price will be greater than $20?

Q: NARRBEGIN: SA_79_83Suppose that the manufacturer of a particular product assesses the joint distribution of the price per unit (P) and demand (D) for its product in the upcoming quarter as presented below. Use this information to answer the following questions. Demand (D)Price per Unit (P) 2000250030003500$200.050.050.030.150.28$250.050.060.100.050.26$300.080.100.040.030.25$350.100.050.030.030.210.280.260.200.26NARRENDWhat is the probability that the demand of this product exceed 2500 units in the upcoming quarter, given that its price will be less than $30?

Q: NARRBEGIN: SA_79_83Suppose that the manufacturer of a particular product assesses the joint distribution of the price per unit (P) and demand (D) for its product in the upcoming quarter as presented below. Use this information to answer the following questions. Demand (D)Price per Unit (P) 2000250030003500$200.050.050.030.150.28$250.050.060.100.050.26$300.080.100.040.030.25$350.100.050.030.030.210.280.260.200.26NARRENDWhat is the probability that the demand of this product will be below its mean in the upcoming quarter?

Q: NARRBEGIN: SA_79_83Suppose that the manufacturer of a particular product assesses the joint distribution of the price per unit (P) and demand (D) for its product in the upcoming quarter as presented below. Use this information to answer the following questions. Demand (D)Price per Unit (P) 2000250030003500$200.050.050.030.150.28$250.050.060.100.050.26$300.080.100.040.030.25$350.100.050.030.030.210.280.260.200.26NARRENDWhat is the probability that the price of this product will be above its mean in the upcoming quarter?

Q: NARRBEGIN: SA_79_83Suppose that the manufacturer of a particular product assesses the joint distribution of the price per unit (P) and demand (D) for its product in the upcoming quarter as presented below. Use this information to answer the following questions. Demand (D)Price per Unit (P) 2000250030003500 $200.050.050.030.150.28$250.050.060.100.050.26$300.080.100.040.030.25$350.100.050.030.030.21 0.280.260.200.26 NARRENDFind the expected price and demand level for the upcoming quarter.

Q: On average, how many customers would you expect to see in each of these two lines at the grocery store?

Q: What is the probability that no more than two customers are waiting in both lines combined?

Q: What is the probability that no one is waiting or being served in the express checkout line?

Q: What is the probability that no one is waiting or being served in the regular checkout line?

Q: Calculate the conditional distribution of Y given X.

Q: (A) Calculate the conditional distribution of X given Y.(B) What is the practical benefit of knowing the conditional distribution in (A)?

Q: NARRBEGIN: SA_70_78A small grocery store has two checkout lines available to its customers: a regular checkout line and an express checkout line. Customers with 5 or fewer items are expected to use the express line. Let X and Y be the number of customers in the regular checkout line and the express checkout line, respectively. Note that these numbers include the customers being served, if any. The joint probability distribution of X and Y is given in the table below.Y = 0Y = 1Y = 23X = 00.060.040.030.15X = 10.090.060.030.04X = 20.080.050.010.1230.070.050.030.09NARRENDFind the marginal distribution of Y. What does this distribution tell you?

Q: NARRBEGIN: SA_70_78A small grocery store has two checkout lines available to its customers: a regular checkout line and an express checkout line. Customers with 5 or fewer items are expected to use the express line. Let X and Y be the number of customers in the regular checkout line and the express checkout line, respectively. Note that these numbers include the customers being served, if any. The joint probability distribution of X and Y is given in the table below. Y = 0Y = 1Y = 23X = 00.060.040.030.15X = 10.090.060.030.04X = 20.080.050.010.1230.070.050.030.09NARRENDFind the marginal distribution of X. What does this distribution tell you?

Q: (A) What is the expected completion time (in months) from now for this project? (B) How much variability (in months) exists around the expected value found in (A)?

Q: NARRBEGIN: SA_61_65 A manufacturing facility needs to open a new assembly line in four months or there will be significant cost overruns. The manager of this project believes that there are four possible values for the random variable X (the number of months from now it will take to complete this project): 3, 3.5, 4, and 4.5. It is currently believed that the probabilities of these four possibilities are in the ratio 1 to 2 to 3 to 2. That is, X = 3.5 is twice as likely as X = 3 and X = 4 is 1.5 times as likely as X = 3.5. NARREND What is the probability that this project will not be completed on time?

Q: NARRBEGIN: SA_61_65 A manufacturing facility needs to open a new assembly line in four months or there will be significant cost overruns. The manager of this project believes that there are four possible values for the random variable X (the number of months from now it will take to complete this project): 3, 3.5, 4, and 4.5. It is currently believed that the probabilities of these four possibilities are in the ratio 1 to 2 to 3 to 2. That is, X = 3.5 is twice as likely as X = 3 and X = 4 is 1.5 times as likely as X = 3.5. NARREND What is the probability that this project will be completed in less than 4 months from now?

Q: NARRBEGIN: SA_61_65A manufacturing facility needs to open a new assembly line in four months or there will be significant cost overruns. The manager of this project believes that there are four possible values for the random variable X (the number of months from now it will take to complete this project): 3, 3.5, 4, and 4.5. It is currently believed that the probabilities of these four possibilities are in the ratio 1 to 2 to 3 to 2. That is, X = 3.5 is twice as likely as X = 3 and X = 4 is 1.5 times as likely as X = 3.5.NARRENDFind the probability distribution of X.

Q: Football teams toss a coin to see who will get their choice of kicking or receiving to begin a game. The probability that given team will win the toss three games in a row is 0.125.

Q: The number of people entering a shopping mall on a given day is an example of a discrete random variable.

Q: If P(A and B) = 0, then A and B must be collectively exhaustive.

Q: Suppose that after graduation you will either buy a new car (event A) or take a trip to Europe (event B). Events A and B are mutually exclusive.

Q: Suppose A and B are two events where P(A) = 0.5, P(B) = 0.4, and P(A and B) = 0.2, then P(B/A) = 0.5.

Q: Suppose A and B are mutually exclusive events where P(A) = 0.3 and P(B) = 0.4, then P(A and B) = 0.12.

Q: The multiplication rule for two events A and B is: P(A and B) = P(A|B)P(A).

Q: The time students spend in a computer lab during one day is an example of a continuous random variable.

Q: Given that events A and B are independent and that P(A) = 0.8 and P(B/A) = 0.4, then P(A and B) = 0.32.

Q: Two or more events are said to be mutually exclusive if at most one of them can occur.

Q: When two events are independent, they are also mutually exclusive.

Q: Two or more events are said to be exhaustive if at most one of them can occur.