Deck 5: Probability

Question 1

If A and B are independent events, then P(A or B) = P(A) P(B).

Answer 1

False

Question 2

When the outcome of a random experiment is a continuous measurement, the sample space is described by a rule instead of listing the possible simple events.

Answer 2

True

Question 3

P(A | B) is the joint probability of events A and B divided by the probability ofA.

Answer 3

False

Question 4

For any event A, the probability of A is always 0 ≤ P(A) ≤ 1.

Question 5

The sum of the probabilities of all compound events in a sample space equals one.

Question 6

The probability of the union of two events P(A or B) can exceed one.

Question 7

Events A and B are mutually exclusive if P(A∩B) = 0.

Question 8

Independent events are mutually exclusive.

Question 9

If events A and B are dependent, it can be concluded that one event causes the other.

Question 10

The odds of an event can be calculated by dividing the event's probability by the probability of its complement.

Question 11

The empirical view of probability is based on relative frequencies.

Question 12

The union of two events A and B is the event consisting of all outcomes in the sample space that are contained in both event A and event B.

Question 13

If events A and B are mutually exclusive, the joint probability of the events is zero.

Question 14

If events A and B are mutually exclusive, then P(A) + P(B) = 0.

Question 15

Grandma's predicting rain based on how much her arthritis is acting up is an example of the classical view of probability.

Question 16

The sum of all the probabilities of simple events in a sample space equals one.

Question 17

A sample space is the set of all possible outcomes in an experiment.

Question 18

Two events A and B are independent if P(A | B) is the same as P(A).

Question 19

Probability is the measure of the relative likelihood that an event will occur.

Question 20

The general law of addition for probabilities says P(A or B) = P(A) + P(B) - P(A∩B).

Question 21

If P(A) = 0.50, P(B) = 0.30, and P(A∩B) = 0.15, then A and B are independent events.

Question 22

Bayes' Theorem shows how to revise a prior probability to obtain a conditional or posterior probability when another event's occurrence is known.

Question 23

A contingency table is a cross-tabulation of frequencies for two categorical variables.

Question 24

The probability of A and its complement (A´) will always sum to one.

Question 25

Two events are mutually exclusive when they contain no outcomes in common.

Question 26

In a contingency table, the probability of the union of two events is found by taking the frequency of the intersection of the two events and dividing by the total.

Question 27

When two events cannot occur at the same time, they are said to be mutually exclusive.

Question 28

Events A and B are mutually exclusive when:

A)their joint probability is zero.
B)they are independent events.
C)P(A)P(B) = 0
D)P(A)P(B) = P(A | B)

Question 29

If A and B are mutually exclusive events, then P(A∩B) = P(A) + P(B).

Question 30

If event A occurs, then its complement (A´) will also occur.

Question 31

The probability of events A or B occurring can be found by summing their probabilities.

Question 32

The number of arrangements of sampled items drawn from a population is found with the formula for permutations (if order is important) or combinations (if order does not matter).

Question 33

If P(A) = .20 then the odds against event A's occurrence are 4 to 1.

Question 34

The general law of addition for probabilities says P(A or B) = P(A) P(B).

Question 35

The value of 7! is 5040.

Question 36

The union of two events is all outcomes in either or both, while the intersection is only those events in both.

Question 37

When two events A and B are independent, the probability of their intersection can be found by multiplying their probabilities.

Question 38

The sum of the probabilities of two mutually exclusive events is one.

Question 39

Insurance company life tables are an example of the classical (a priori) approach to probability.

Question 40

P(A∩B) = .50 is an example of a joint probability.

Question 41

Given the contingency table shown here, find P(V | W). $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Cell Phone Service Provider }\\\begin{array}{|c|c|c|c|c|}\hline County&\text { Sprint }(S) &\text { AT\&T }(A)& \text { Verizon }(I)& \text { Row Total }\\\hline Macomb (M) &17 & 25 & 8 & 50 \\\hline Oakland (O) &19 & 38 & 13 & 70 \\\hline Wayne (W) &24 & 37 & 19 & 80 \\\hline Col Total &60 & 100 & 40 & 200 \\\hline\end{array}\end{array}$

A).4000
B).0950
C).2375
D).5875

Question 42

Independent events A and B would be consistent with which of the following statements:

A)P(A) = .3, P(B) = .5, P(A∩B) = .4.
B)P(A) = .4, P(B) = .5, P(A∩B) = .2.
C)P(A) = .5, P(B) = .4, P(A∩B) = .3.
D)P(A) = .4, P(B) = .3, P(A∩B) = .5.

Question 43

Given the contingency table shown here, find P(A or B). $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Age }$
$\begin{array} {| l | c | c | c| } \hline\text { Absences } & \text { Under } 25 ( A ) & 25 \text { or More } \left( A ^ { \prime } \right) & \text { Row Total } \\\hline \text { Under } 2 \text { days } ( B ) & 50 & 40 & 90 \\\hline 2 \text { or more days } \left( B ^ { \prime } \right) & 30 & 80 & 110 \\\hline \text { Column Total } & 80 & 120 & 200\\\hline\end{array}$

A).25
B).85
C).60
D).42

Question 44

Find the probability that either event A or B occurs if the chance of A occurring is .5, the chance of B occurring is .3, and events A and B are independent.

A).80
B).15
C).65
D).85

Question 45

If two events are complementary, then we know that:

A)the sum of their probabilities is one.
B)the joint probability of the two events is one.
C)their intersection has a nonzero probability.
D)they are independent events.

Question 46

Given the contingency table shown here, find P(A₂ | B₃). $$\begin{array} { |c | c | c | c | c | c | } \hline{ } & { A _ { 1 } } & A _ { 2 } & A _ { 3 } & A _ { 4 } & \text { Row Total } \\\hline B _ { 1 } & 12 & 26 & 42 & 68&148 \\\hline B _ { 2 } & 14 & 28 & 44 & 64 &150\\\hline B _ { 3 } & 18 & 32 & 47 & 72 &169\\\hline \text { Col Total } & 44 & 86 & 133 & 204 & 467 \\\hline\end{array}$$

A).0685
B).1893
C).3721
D).1842

Question 47

Given the contingency table shown here, find P(A or M). $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Cell Phone Service Provider }\\\begin{array}{|c|c|c|c|c|}\hline County&\text { Sprint }(S) &\text { AT\&T }(A)& \text { Verizon }(I)& \text { Row Total }\\\hline Macomb (M) &17 & 25 & 8 & 50 \\\hline Oakland (O) &19 & 38 & 13 & 70 \\\hline Wayne (W) &24 & 37 & 19 & 80 \\\hline Col Total &60 & 100 & 40 & 200 \\\hline\end{array}\end{array}$

A).2500
B).7500
C).6250
D).1250

Question 48

Given the contingency table shown here, find P(A₂). $$\begin{array} { |c | c | c | c | c | c | } \hline{ } & { A _ { 1 } } & A _ { 2 } & A _ { 3 } & A _ { 4 } & \text { Row Total } \\\hline B _ { 1 } & 12 & 26 & 42 & 68&148 \\\hline B _ { 2 } & 14 & 28 & 44 & 64 &150\\\hline B _ { 3 } & 18 & 32 & 47 & 72 &169\\\hline \text { Col Total } & 44 & 86 & 133 & 204 & 467 \\\hline\end{array}$$

A).1842
B).1766
C).8163
D).0578

Question 49

Given the contingency table shown here, find P(W?S). $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Cell Phone Service Provider }\\\begin{array}{|c|c|c|c|c|}\hline County&\text { Sprint }(S) &\text { AT\&T }(A)& \text { Verizon }(I)& \text { Row Total }\\\hline Macomb (M) &17 & 25 & 8 & 50 \\\hline Oakland (O) &19 & 38 & 13 & 70 \\\hline Wayne (W) &24 & 37 & 19 & 80 \\\hline Col Total &60 & 100 & 40 & 200 \\\hline\end{array}\end{array}$

A).12
B).30
C).40
D).58

Question 50

Regarding probability, which of the following is correct?

A)When events A and B are mutually exclusive, then P(A∩B) = P(A) + P(B).
B)The union of events A and B consists of all outcomes in the sample space that are contained in both event A and event B.
C)When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events.
D)The probability of the union of two events can exceed one.

Question 51

Given the contingency table shown here, find P(V). $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Cell Phone Service Provider }\\\begin{array}{|c|c|c|c|c|}\hline County&\text { Sprint }(S) &\text { AT\&T }(A)& \text { Verizon }(I)& \text { Row Total }\\\hline Macomb (M) &17 & 25 & 8 & 50 \\\hline Oakland (O) &19 & 38 & 13 & 70 \\\hline Wayne (W) &24 & 37 & 19 & 80 \\\hline Col Total &60 & 100 & 40 & 200 \\\hline\end{array}\end{array}$

A).20
B).40
C).50
D).80

Question 52

Within a given population, 22 percent of the people are smokers, 57 percent of the people are males, and 12 percent are males who smoke. If a person is chosen at random from the population, what is the probability that the selected person is either a male or a smoker?

A).67
B).79
C).22
D).43

Question 53

Given the contingency table shown here, find P(B). $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Age }$
$\begin{array} {| l | c | c | c| } \hline\text { Absences } & \text { Under } 25 ( A ) & 25 \text { or More } \left( A ^ { \prime } \right) & \text { Row Total } \\\hline \text { Under } 2 \text { days } ( B ) & 50 & 40 & 90 \\\hline 2 \text { or more days } \left( B ^ { \prime } \right) & 30 & 80 & 110 \\\hline \text { Column Total } & 80 & 120 & 200\\\hline\end{array}$

A).85
B).25
C).45
D).22

Question 54

Given the contingency table shown here, find the probability that either event A₂ or event B₂ will occur. $$\begin{array} { |c | c | c | c | c | c | } \hline{ } & { A _ { 1 } } & A _ { 2 } & A _ { 3 } & A _ { 4 } & \text { Row Total } \\\hline B _ { 1 } & 12 & 26 & 42 & 68&148 \\\hline B _ { 2 } & 14 & 28 & 44 & 64 &150\\\hline B _ { 3 } & 18 & 32 & 47 & 72 &169\\\hline \text { Col Total } & 44 & 86 & 133 & 204 & 467 \\\hline\end{array}$$

A).4454
B).5054
C).0600

Question 55

Given the contingency table shown here, find P(A₁?A₂). $$\begin{array} { |c | c | c | c | c | c | } \hline{ } & { A _ { 1 } } & A _ { 2 } & A _ { 3 } & A _ { 4 } & \text { Row Total } \\\hline B _ { 1 } & 12 & 26 & 42 & 68&148 \\\hline B _ { 2 } & 14 & 28 & 44 & 64 &150\\\hline B _ { 3 } & 18 & 32 & 47 & 72 &169\\\hline \text { Col Total } & 44 & 86 & 133 & 204 & 467 \\\hline\end{array}$$

A).00
B).09
C).28
D).38

Question 56

Regarding the rules of probability, which of the following statements is correct?

A)If A and B are independent events, then P(B) = P(A)P(B).
B)The sum of two mutually exclusive events is one.
C)The probability of A and its complement will sum to one.
D)If event A occurs, then its complement will also occur.

Question 57

Information was collected on those who attended the opening of a new movie. The analysis found that 56 percent of the moviegoers were female, 26 percent were under age 25, and 17 percent were females under the age of 25. Find the probability that a moviegoer is either female or under age 25.

A).79
B).82
C).65
D).50

Question 58

Given the contingency table shown here, find the probability P(V´), that is, the probability of the complement of V. $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Cell Phone Service Provider }\\\begin{array}{|c|c|c|c|c|}\hline County&\text { Sprint }(S) &\text { AT\&T }(A)& \text { Verizon }(I)& \text { Row Total }\\\hline Macomb (M) &17 & 25 & 8 & 50 \\\hline Oakland (O) &19 & 38 & 13 & 70 \\\hline Wayne (W) &24 & 37 & 19 & 80 \\\hline Col Total &60 & 100 & 40 & 200 \\\hline\end{array}\end{array}$

A).30
B).50
C).80
D).15

Question 59

Given the contingency table shown here, find P(A₁ or B₂). $$\begin{array} { |c | c | c | c | c | c | } \hline{ } & { A _ { 1 } } & A _ { 2 } & A _ { 3 } & A _ { 4 } & \text { Row Total } \\\hline B _ { 1 } & 12 & 26 & 42 & 68&148 \\\hline B _ { 2 } & 14 & 28 & 44 & 64 &150\\\hline B _ { 3 } & 18 & 32 & 47 & 72 &169\\\hline \text { Col Total } & 44 & 86 & 133 & 204 & 467 \\\hline\end{array}$$

A).0933
B).3182
C).0300
D).3854

Question 60

Given the contingency table shown here, find P(A₃?B₂). $$\begin{array} { |c | c | c | c | c | c | } \hline{ } & { A _ { 1 } } & A _ { 2 } & A _ { 3 } & A _ { 4 } & \text { Row Total } \\\hline B _ { 1 } & 12 & 26 & 42 & 68&148 \\\hline B _ { 2 } & 14 & 28 & 44 & 64 &150\\\hline B _ { 3 } & 18 & 32 & 47 & 72 &169\\\hline \text { Col Total } & 44 & 86 & 133 & 204 & 467 \\\hline\end{array}$$

A).3212
B).2933
C).0942
D).1006

Question 61

Oxnard Casualty wants to ensure that their e-mail server has 99.98 percent reliability. They will use several independent servers in parallel, each of which is 95 percent reliable. What is the smallest number of independent file servers that will accomplish the goal?

A)1
B)2
C)3
D)4

Question 62

Given the contingency table shown here, what is the probability that a student attends a public school in a rural area? $$\text { What type of school do you attend? }$$
$\begin{array}{|c|c|c|c|c|}\hline \text { Location } &\text { Public }(P) & \text { Religious }(R) & \text { Other Private }(O) & \text { Row Total } \\\hline \text { Inner City (I) }&35 & 15 & 20&70 \\\hline \text { Sububan (S) }&45 & 10 & 25&80 \\\hline \text { Rural (R) }&25 & 5 & 5&35 \\\hline \text { Col Total }& 105 & 30 & 50&185 \\\hline\end{array}$

A).238
B).714
C).135
D).567

Question 63

Given the contingency table shown here, what is the probability that a participant selected at random is a graduate student who opposes the change to a quarter system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Surveyed }$

$\begin{array}{|c|c|c|c|c|}\hline \text { Opinion: } &\text { Undergrads }(U) & \text { Graduates }(G) & \text { Faculty }(F)& \text { Row Total } \\\hline \text { Oppose Change (N) } &73 & 27 & 20&120 \\\hline \text { Favor Change (S) } &27 & 23 & 30&80 \\\hline \text { Col Total } &100 & 50 & 50&200 \\\hline\end{array}$

A).135
B).250
C).375
D).540

Question 64

Given the contingency table shown here, find P(B | A). $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Age }$
$\begin{array} {| l | c | c | c| } \hline\text { Absences } & \text { Under } 25 ( A ) & 25 \text { or More } \left( A ^ { \prime } \right) & \text { Row Total } \\\hline \text { Under } 2 \text { days } ( B ) & 50 & 40 & 90 \\\hline 2 \text { or more days } \left( B ^ { \prime } \right) & 30 & 80 & 110 \\\hline \text { Column Total } & 80 & 120 & 200\\\hline\end{array}$

A).250
B).555
C).855
D).625

Question 65

Given the contingency table shown here, if a randomly chosen student attends a religious school, what is the probability the location is rural?
$$\text { What type of school do you attend? }$$
$\begin{array}{|c|c|c|c|c|}\hline \text { Location } &\text { Public }(P) & \text { Religious }(R) & \text { Other Private }(O) & \text { Row Total } \\\hline \text { Inner City (I) }&35 & 15 & 20&70 \\\hline \text { Sububan (S) }&45 & 10 & 25&80 \\\hline \text { Rural (R) }&25 & 5 & 5&35 \\\hline \text { Col Total }& 105 & 30 & 50&185 \\\hline\end{array}$

A).142
B).162
C).167
D).333

Question 66

Ramjac Company wants to set up k independent file servers, each capable of running the company's intranet. Each server has average "uptime" of 98 percent. What must k be to achieve 99.999 percent probability that the intranet will be "up"?

A)1
B)2
C)3
D)4

Question 67

Given the contingency table shown here, find P(W | M). Survey question: Do you plan on retiring or keep working when you turn 65? $$\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$$

A).145
B).250
C).581
D).687

Question 68

Given the contingency table shown here, find P(L or W). Survey question: Do you plan on retiring or keep working when you turn 65? $$\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$$

A).750
B).588
C).435
D).895

Question 69

Given the contingency table shown here, find P(R?L). Survey question: Do you plan on retiring or keep working when you turn 65? $$\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$$

A).250
B).315
C).425
D).850

Question 70

Given the contingency table shown here, what is the probability that a mother in the study smoked during pregnancy? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$

$\begin{array}{|c|r|r|r|}\hline \text { Mother's Education } & \text { Pregnancy } & \text { Pregnancy } & \text { Row Total } \\\hline\text { Below High School } &393 & 640 &1,033\\\hline \text { High School }&560 & 1,370&1,930 \\\hline \text { Some College }&121 & 635 &756\\\hline\text { College Degree} &48 & 550 &598\\\hline \text { Col Total } &1,122 & 3,209&4,331\\\hline\end{array}$

A).2591
B).3174
C).5000
D).7401

Question 71

Given the contingency table shown here, what is the probability that a mother smoked during pregnancy and had a college degree? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$

$\begin{array}{|c|r|r|r|}\hline \text { Mother's Education } & \text { Pregnancy } & \text { Pregnancy } & \text { Row Total } \\\hline\text { Below High School } &393 & 640 &1,033\\\hline \text { High School }&560 & 1,370&1,930 \\\hline \text { Some College }&121 & 635 &756\\\hline\text { College Degree} &48 & 550 &598\\\hline \text { Col Total } &1,122 & 3,209&4,331\\\hline\end{array}$

A).0111
B).0428
C).0803
D).2385

Question 72

Given the contingency table shown here, if a survey participant is selected at random, what is the probability he/she is an undergrad who favors the change to a quarter system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Surveyed }$

$\begin{array}{|c|c|c|c|c|}\hline \text { Opinion: } &\text { Undergrads }(U) & \text { Graduates }(G) & \text { Faculty }(F)& \text { Row Total } \\\hline \text { Oppose Change (N) } &73 & 27 & 20&120 \\\hline \text { Favor Change (S) } &27 & 23 & 30&80 \\\hline \text { Col Total } &100 & 50 & 50&200 \\\hline\end{array}$

A).270
B).135
C).338
D).756

Question 73

Given the contingency table shown here, if a faculty member is chosen at random, what is the probability he/she opposes the change to a quarter system? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Surveyed }$

$\begin{array}{|c|c|c|c|c|}\hline \text { Opinion: } &\text { Undergrads }(U) & \text { Graduates }(G) & \text { Faculty }(F)& \text { Row Total } \\\hline \text { Oppose Change (N) } &73 & 27 & 20&120 \\\hline \text { Favor Change (S) } &27 & 23 & 30&80 \\\hline \text { Col Total } &100 & 50 & 50&200 \\\hline\end{array}$

A).10
B).25
C).40
D).60

Question 74

Given the contingency table shown here, what is the probability that a mother smoked during pregnancy or that she graduated from college? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$

$\begin{array}{|c|r|r|r|}\hline \text { Mother's Education } & \text { Pregnancy } & \text { Pregnancy } & \text { Row Total } \\\hline\text { Below High School } &393 & 640 &1,033\\\hline \text { High School }&560 & 1,370&1,930 \\\hline \text { Some College }&121 & 635 &756\\\hline\text { College Degree} &48 & 550 &598\\\hline \text { Col Total } &1,122 & 3,209&4,331\\\hline\end{array}$

A).0111
B).2591
C).3861
D).7850

Question 75

Given the contingency table shown here, find the probability that a randomly chosen employee is a line worker who plans to retire at age 65. Survey question: Do you plan on retiring or keep working when you turn 65? $$\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$$

A).227
B).419
C).750
D).315

Question 76

Given the contingency table shown here, find the probability that a mother with some college smoked during pregnancy. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$

$\begin{array}{|c|r|r|r|}\hline \text { Mother's Education } & \text { Pregnancy } & \text { Pregnancy } & \text { Row Total } \\\hline\text { Below High School } &393 & 640 &1,033\\\hline \text { High School }&560 & 1,370&1,930 \\\hline \text { Some College }&121 & 635 &756\\\hline\text { College Degree} &48 & 550 &598\\\hline \text { Col Total } &1,122 & 3,209&4,331\\\hline\end{array}$

A).1078
B).1746
C).1601
D).1117

Question 77

Given the contingency table shown here, what is the probability that a randomly chosen employee who is under age 25 would be absent 2 or more days? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Age }$
$\begin{array} {| l | c | c | c| } \hline\text { Absences } & \text { Under } 25 ( A ) & 25 \text { or More } \left( A ^ { \prime } \right) & \text { Row Total } \\\hline \text { Under } 2 \text { days } ( B ) & 50 & 40 & 90 \\\hline 2 \text { or more days } \left( B ^ { \prime } \right) & 30 & 80 & 110 \\\hline \text { Column Total } & 80 & 120 & 200\\\hline\end{array}$

A).625
B).375
C).150
D).273

Question 78

Given the contingency table shown here, does the decision to retire appear independent of the employee type? Survey question: Do you plan on retiring or keep working when you turn 65? $$\begin{array} { | l | c | c | c | } \hline\text { Employee } & \text { Retire } ( R ) & \text { Work } ( W ) & \text { Total }\\\hline \text { Management } ( M ) & 13 & 18 &31 \\\hline \text { Line worker } ( L ) & 39 & 54 & 93 \\\hline \text { Total } & 52 & 72 & 124\\\hline\end{array}$$

A)Yes.
B)No.

Question 79

Given the contingency table shown here, if a mother attended some college but did not have a degree, what is the probability that she did not smoke during her pregnancy? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$

$\begin{array}{|c|r|r|r|}\hline \text { Mother's Education } & \text { Pregnancy } & \text { Pregnancy } & \text { Row Total } \\\hline\text { Below High School } &393 & 640 &1,033\\\hline \text { High School }&560 & 1,370&1,930 \\\hline \text { Some College }&121 & 635 &756\\\hline\text { College Degree} &48 & 550 &598\\\hline \text { Col Total } &1,122 & 3,209&4,331\\\hline\end{array}$

A).2736
B).8399
C).8752
D).9197

Question 80

Given the contingency table shown here, what is the probability that a mother smoked during pregnancy if her education level was below high school? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Smoked during }$$\quad$ $\text { Didn't Smoke during }$

$\begin{array}{|c|r|r|r|}\hline \text { Mother's Education } & \text { Pregnancy } & \text { Pregnancy } & \text { Row Total } \\\hline\text { Below High School } &393 & 640 &1,033\\\hline \text { High School }&560 & 1,370&1,930 \\\hline \text { Some College }&121 & 635 &756\\\hline\text { College Degree} &48 & 550 &598\\\hline \text { Col Total } &1,122 & 3,209&4,331\\\hline\end{array}$

A).2385
B).0907
C).3503
D).3804