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Homework answers / question archive / 1) Describe what the notation P(B |A) represents
1) Describe what the notation P(B |A) represents.
Choose the correct answer below.
A. The probability of event B and event A occurring.
B. The probability of event A occurring, given that event B has already occurred.
C. The probability of event B occurring, given that event A has already occurred.
D. The probability of event B or event A occurring.
2) For the given pair of events A and B, complete parts (a) and (b) below.
A: When a page is randomly selected and ripped from a 5-page document and destroyed, it is page 1.
B: When a different page is randomly selected and ripped from the document, it is page 4.
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur.
a. Choose the correct answer below.
A. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.
B. The two events are independent because the 5% guideline indicates that they should be treated as independent.
C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
b. The probability that events A and B both occur is 0.0500 .
(Round to four decimal places as needed.)
YOU ANSWER: 1/410
3) For the given pair of events A and B, complete parts (a) and (b) below.
A: When a baby is born, it is a boy.
B: When a 4-sided die is rolled, the outcome is 3.
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur.
a. Choose the correct answer below.
A. The two events are independent because the 5% guideline indicates that they may be treated as independent.
B. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.
C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
b. The probability that events A and B both occur is .1250 .
(Round to four decimal places as needed.)
4) Consider a bag that contains 228 coins of which 6 are rare Indian pennies. For the given pair of events A and B, complete parts (a) and (b) below.
A: When one of the 228 coins is randomly selected, it is one of the 6 Indian pennies.
B: When another one of the 228 coins is randomly selected (with replacement), it is also one of the 6 Indian pennies.
a. Determine whether events A and B are independent or dependent.
b. Find P(A and B), the probability that events A and B both occur.
a. Choose the correct answer below.
A. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
B. The two events are independent because the 5% guideline indicates that they may be treated as independent.
C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
D. The two events are dependent because the 5% guideline indicates that they may be treated as dependent.
b. The probability that events A and B both occur is 0.000692 .
(Round to six decimal places as needed.)
5) For the given pair of events A and B, complete parts (a) and (b) below.
A: A marble is randomly selected from a bag containing 14 marbles consisting of 1 red, 9 blue, and 4 green marbles. The selected marble is one of the green marbles.
B: A second marble is selected and it is the 1 red marble in the bag.
a. Determine whether events A and B are independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)
b. Find P(A and B), the probability that events A and B both occur.
a. Choose the correct answer below.
A. The two events are independent because the 5% guideline can be applied in this case.
B. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
C. The two events are dependent because the occurrence of one affects the probability of the
D. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other and the 5% guideline cannot be applied in this case.
b. The probability that events A and B both occur is 0.0220 .
(Round to four decimal places as needed.)
YOU ANSWERED: .0275
6) Refer to the table below. Given that 2 of the 108 subjects are randomly selected, complete parts (a) and (b).
|
|
Group |
|||
|
|
O |
A |
B |
AB |
|
Rh+ Type Rh- |
37
8 |
34
6 |
11
1 |
10
1 |
a. Assume that the selections are made with replacement. What is the probability that the 2 selected subjects are both group AB and type Rh+?
0.0086 (Round to four decimal places as needed.)
b. Assume the selections are made without replacement. What is the probability that the 2 selected subjects are both group AB and type Rh+?
0.0078 (Round to four decimal places as needed.)
YOU ANSWERED: 0.0961
9
7) The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts (a) and (b) below. Are these events unlikely?
a. Four of the test subjects are randomly selected with replacement, and they all had true negative test results.
b. Four of the test subjects are randomly selected without replacement, and they all had true negative test results.
Click on the icon to view the data table.
a. The probability that all four test subjects had a true negative test result when they are randomly selected with replacement is 0.044 .
(Round to three decimal places as needed.)
Is such an event unlikely?
A. Yes, because the probability of the event is less than 0.05.
B. No, because the probability of the event is less than 0.05.
C. No, because the probability of the event is greater than 0.05.
D. Yes, because the probability of the event is greater than 0.05.
b. The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is 0.040 .
(Round to three decimal places as needed.)
Is such an event unlikely?
A. No, because the probability of the event is greater than 0.05.
B. Yes, because the probability of the event is less than 0.05.
C. Yes, because the probability of the event is greater than 0.05.
D. No, because the probability of the event is less than 0.05.
1: Polygraph Test Results
|
|
No (Did Not Lie) |
Yes (Lied) |
|
Positive test result |
9 |
21 |
|
(Positive test indicated that the subject lied.) |
(false positive) |
(true positive) |
|
Negative test result |
38 |
15 |
|
(Polygraph test indicated that the subject did not lie.) |
(true negative) |
(false negative) |
YOU ANSWERED: 0.4580
B.
5
D.
8) With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. A company has just manufactured 656 CDs, and 138 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted? Does this outcome suggest that the entire batch consists of good CDs? Why or why not?
If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
The probability that the whole batch is accepted is ? .
(Round to three decimal places as needed.)
Does the result in (a) suggest that the entire batch consists of good CDs? Why or why not?
A. Yes, because if all three CDs in the sample are good then the entire batch must be good.
B. No, because the sample will always consist of good CDs.
C. No, because only a probability of 1 would indicate the entire batch consists of good CDs.
D. Yes, because it is not unlikely that the batch will be accepted.
9) 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 17.2% daily failure rate. Complete parts (a) through (d) below.
a. What is the probability that the student's alarm clock will not work on the morning of an important final exam?
0.172 (Round to three decimal places as needed.)
b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
0.02958 (Round to five decimal places as needed.)
c. What is the probability of not being awakened if the student uses three independent alarm clocks?
0.00509 (Round to five decimal places as needed.)
d. Do the second and third alarm clocks result in greatly improved reliability?
A. No, because the malfunction of both is equally or more likely than the malfunction of one.
B. Yes, because you can always be certain that at least one alarm clock will work.
C. Yes, because total malfunction would not be impossible, but it would be unlikely.
D. No, because total malfunction would still not be unlikely.
YOU ANSWERED: .087
0.0296
0.00500
10) The principle of redundancy is used when system reliability is improved through redundant or backup components. A region's government requires that commercial aircraft used for flying in hazardous conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.004. What is the probability that a particular flight will be threatened with the failure of both radios? Describe how the second independent radio increases safety in this case.
What is the probability that a particular flight will be threatened with the failure of both radios?
(Round to six decimal places as needed.)
Describe how the second independent radio increases safety in this case. Choose the correct answer below.
A. The second radio makes it impossible for the airplane to crash.
B. The second radio has no effect on safety.
C. With one radio there is a 0.004 probability of a serious problem, but with two independent radios, the probability of a serious problem decreases substantially. The flight becomes much safer with two independent radios.
D. With one radio there is a 0.004 probability of a serious problem, but with two independent radios, the probability of a serious problem increases substantially. The flight becomes much less safe with two independent radios.
11) Assume that a company hires employees on Mondays, Tuesdays, or Wednesdays with equal likelihood. Complete parts (a) through (c) below.
a. If two different employees are randomly selected, what is the probability that they were both hired on a Tuesday?
The probability is ?.
(Type an integer or a simplified fraction.)
b. If two different employees are randomly selected, what is the probability that they were both hired on the same day of the week?
The probability is ?.
(Type an integer or a simplified fraction.)
c. What is the probability that 5 people in the same department were all hired on the same day of the week? Is such an event unlikely?
The probability is ?.
(Type an integer or a simplified fraction.)
Is such an event unlikely?
A. No, because the probability that all 5 people were hired on the same day of the week is less than or equal to 0.05.
B. No, because the probability that all 5 people were hired on the same day of the week is greater than 0.05.
C. Yes, because the probability that all 5 people were hired on the same day of the week is greater than 0.05.
D. Yes, because the probability that all 5 people were hired on the same day of the week is less than or equal to 0.05.
12) The data in the table below summarize results from 75 pedestrian deaths that were caused by accidents. If two different deaths are randomly selected without replacement, find the probability that they both involved intoxicated drivers. Is such an event unlikely?
|
|
Pedestrian Intoxicated? |
||
|
Yes |
No |
||
|
Driver Intoxicated? |
Yes |
16 |
33 |
|
No |
5 |
21 |
|
The probability is ?.
(Round to three decimal places as needed.)
Is such an event unlikely?
A. Yes, because its probability is less than 0.05.
B. Yes, because its probability is greater than 0.05.
C. No, because its probability is greater than 0.05.
D. No, because its probability is less than 0.05.
13) The data in the following table summarize results from 115 pedestrian deaths that were caused by accidents. If three different deaths are randomly selected without replacement, find the probability that they all involved intoxicated drivers.
|
|
Pedestrian Intoxicated? |
||
|
Yes |
No |
||
|
Driver Intoxicated? |
Yes |
16 |
43 |
|
No |
13 |
43 |
|
The probability is ?.
(Round to six decimal places as needed.)
Is such an event unlikely?
A. No, because its probability is greater than 0.05.
B. Yes, because its probability is greater than 0.05.
C. No, because its probability is less than 0.05.
D. Yes, because its probability is less than 0.05.
14) In a market research survey of 2514 motorists, 276 said that they made an obscene gesture in the previous month. Complete parts (a) and (b) below.
a. If 1 of the surveyed motorists is randomly selected, what is the probability that this motorist did not make an obscene gesture in the previous month?
The probability is ?. (Round to four decimal places as needed.)
b. If 45 of the surveyed motorists are randomly selected without replacement, what is the probability that none of them made an obscene gesture in the previous month? Should the 5% guideline be applied in this case? Select the correct choice below and fill in the answer box within your choice.
(Round to four decimal places as needed.)
A. The probability is _____________. The 5% guideline should be applied in this case.
B. The probability is __________. The 5% guideline should not be applied in this case.
15) A tire company produced a batch of 6,300 tires that includes exactly 300 that are defective.
a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?
b. If 100 tires are randomly selected for shipment to an outlet, what is the probability that they are all good? Should this outlet plan to deal with defective tires returned by consumers?
a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good?
(Round to three decimal places as needed.)
b. If 100 tires are randomly selected for shipment to an outlet what is the probability that they are all good?
(Round to three decimal places as needed.)
Should this outlet plan to deal with defective tires returned by consumers?
A. No, because there is a very small chance that all 100 tires are good.
B. Yes, because there is a very small chance that all 100 tires are good.
C. No, because there is a very large chance that all 100 tires are good.
D. Yes, because there is a very large chance that all 100 tires are good.
16) 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. Complete parts (a) through (c) below.
a. If the two surge protectors are arranged in series, what is the probability that a voltage surge will not damage the television?
(Do not round.)
b. If the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television?
(Do not round.)
c. Which arrangement should be used for better protection?
17) Which word is associated with multiplication when computing probabilities?
Choose the correct answer below.
Not
And
Or
Disjoint
18) Fill in the blank.
A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a _______.
A picture of line segments branching out from one starting point illustrating the possible outcomes of a procedure is called a tree diagram.
19) What does P(B|A) represent?
Choose the correct answer below.
A. The probability of event A occurring after it is assumed that event B has already occurred
B. The probability of event A or event B or both occurring
C. The probability of event A and event B both occurring
D. The probability of event B occurring after it is assumed that event A has already occurred
20) Fill in the blank.
Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
Two events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other.
21) Fill in the blank.
Selections made with replacement are considered to be _______.
Selections made with replacement are considered to be independent.
