Stat 4.2 HW

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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 direct​in-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.


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