Stat 4.2 HW
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.1% daily failure rate. What is the probability of not being awakened if the student uses three independent alarm clocks?
0.00417
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.1% daily failure rate. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
0.02592
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 340, 276, 243, 146 Order Not Accurate: 34, 58, 35, 13 If three different orders are selected, find the probability that they are all from restaurant A.
0.0346
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 311, 263, 249, 133 Order Not Accurate: 33, 51, 36, 18 If one order is selected, find the probability of getting an order that is not accurate.
0.126
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.1% daily failure rate. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
0.161
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 331, 274, 234, 133 Order Not Accurate: 38, 55, 39, 10 If one order is selected, find the probability of getting an order that is not accurate or is from Restaurant C.
0.338
In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)=0.570, where D is directly in person. What does P(D̅) represent?
0.43
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 335, 280, 244, 122 Order Not Accurate: 35, 54, 31, 19 If one order is selected, find the probability of getting an order from restaurant A or D or an order that is not accurate.
0.532
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 142 subjects with positive test results, there are 22 false positive results; among 150 negative results, there are 4 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana.
0.589
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 140 subjects with positive test results, there are 30 false positive results. Among 159 negative results, there are 3 false negative results. What is the probability that a randomly selected subject did not use marijuana?
0.622
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 333, 261, 244, 146 Order Not Accurate: 31, 53, 38, 18 If one order is selected, find the probability of getting food that is not from Restaurant A.
0.676
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.91 probability of working correctly when a voltage surge occurs. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television?
0.8281
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 325, 275, 246, 127 Order Not Accurate: 31, 56, 32, 10 If one order is selected, find the probability of getting an order from Restaurant A or an order that is accurate.
0.911
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.91 probability of working correctly when a voltage surge occurs. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television?
0.9919
Find the indicated complement. A certain group of women has a 0.32% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
0.9968
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 140 subjects with positive test results, there are 30 false positive results. Among 159 negative results, there are 3 false negative results. How many subjects did not use marijuana?
186
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 140 subjects with positive test results, there are 30 false positive results. Among 159 negative results, there are 3 false negative results. How many subjects were included in the study?
299
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P (B or B̅) = 1
It is certain that the selected adult has type B blood or does not have type B blood.
When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. Is P(M|B) the same as P(B|M)?
No, because P(B|M) represents the probability of getting someone with blue eyes, given that a male has been selected.
In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)=0.570, where D is directly in person. If someone is randomly selected, what does P(D̅) represent?
P(D̅) is the probability of randomly selecting someone who does not choose a directin-person encounter as the most fun way to flirt.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 325, 275, 246, 127 Order Not Accurate: 31, 56, 32, 10 Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events?
The events are not disjoint because it is possible to receive an accurate order from Restaurant A.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 331, 274, 234, 133 Order Not Accurate: 38, 55, 39, 10 Are the events of selecting an order that is not accurate and selecting an order from Restaurant C disjoint events?
The events are not disjoint because it is possible to receive an inaccurate order from Restaurant C.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 339, 272, 230, 123 Order Not Accurate: 36, 56, 32, 11 If two orders are selected, find the probability that they are both accurate. Assume that the selections are made with replacement. Are the events independent?
The probability 0.7694. The events are independent.
Among 6649 cases of heart pacemaker malfunctions, 360 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3 different pacemakers randomly selected from this batch of 6649 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
The probability is 0.846. This procedure is likely to result in the entire batch being accepted.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 339, 272, 230, 123 Order Not Accurate: 36, 56, 32, 11 If two orders are selected, find the probability that they are both accurate. Assume that the selections are made without replacement. Are the events independent?
The probability is 0.7693. The events are not independent.
In a study of helicopter usage and patient survival, among the 47,861 patients transported by helicopter, 201 of them left the treatment center against medical advice, and the other 47,660 did not leave against medical advice. If 60 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left the treatment center against medical advice?
The probability is 0.777
What does P(B|A) represent?
The probability of event B occurring after it is assumed that event A has already occurred
When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent?
The probability of getting a male, given that someone with blue eyes has been selected.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 332, 280, 242, 124 Order Not Accurate: 36, 52, 37, 20 If two orders are selected, find the probability that they are both from Restaurant D. Assume that the selections are made without replacement. Are the events independent?
The probability of getting two orders from Restaurant D is 0.0163. The events are not independent because choosing the first order affects the probability of the choice of the second order.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Restaurant A Restaurant B Restaurant C Restaurant D Order Accurate: 332, 280, 242, 124 Order Not Accurate: 36, 52, 37, 20 If two orders are selected, find the probability that they are both from Restaurant D. Assume that the selections are made with replacement. Are the events independent?
The probability of getting two orders from Restaurant D is 0.0164. The events are independent because choosing the first order does not affect the probability of the choice of the second order.
There are 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without replacement, are the selections independent or dependent?
The selections are dependent, because the selection is done without replacement.
Refer to the figure below in which surge protectors p and q are used to protect an expensive high-definition television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.91 probability of working correctly when a voltage surge occurs. Which arrangement should be used for better protection?
The series arrangement provides better protection because it has a higher probability of protection.
There are 15,958,866 adults in a region. If the selections are dependent, can they be treated as independent for the purposes of calculations?
Yes, because the sample size is less than 5% of the population.
When using the _______ always be careful to avoid double-counting outcomes.
addition rule
A _______ is any event combining two or more simple events.
compound event
Events that are _______ cannot occur at the same time
disjoint
Selections made with replacement are considered to be _______.
independent
Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
independent
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What does P(Ā) represent?
probability of selecting an adult who does not have blue eyes.
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What does P(A) represent?
probability of selecting an adult with blue eyes.
P(A)+P(A̅) = 1 is one way to express the _______
rule of complementary events
P(A or B) indicates _______
the probability that in a single trial, event A occurs, event B occurs, or they both occur.
A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______.
tree diagram
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.1% daily failure rate. Do the second and third alarm clocks result in greatly improved reliability?
Yes, because total malfunction would not be impossible, but it would be unlikely.
