Categorical Data and Conditional Probabilities SAT Practice

MathChapter 9: Categorical Data and Probability

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Question 1 of 50

Question 1

Easy

According to the displayed table, what is the total number in the Bus row?

Selected condition: Use the Bus row.

Commute method and arrival status
Commute method / Arrival status	On time	Late	Total
Bus	36	9	45
Walk	28	4	32
Bicycle	22	6	28
Total	86	19	105

\(45\)\(36\)\(86\)\(105\)

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Question 2 of 50

Question 2

Easy

According to the displayed table, what is the total number in the On time column?

Selected condition: Use the On time column.

Commute method and arrival status
Commute method / Arrival status	On time	Late	Total
Bus	36	9	45
Walk	28	4	32
Bicycle	22	6	28
Total	86	19	105

\(36\)\(86\)\(45\)\(105\)

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Question 3 of 50

Question 3

Easy

If one observation is selected from the full table, what is the probability it is both Bus AND On time?

Selected condition: Bus AND On time: use the labeled intersection cell.

Commute method and arrival status
Commute method / Arrival status	On time	Late	Total
Bus	36	9	45
Walk	28	4	32
Bicycle	22	6	28
Total	86	19	105

\(\frac{4}{5}\)\(\frac{18}{43}\)\(\frac{12}{35}\)\(\frac{3}{7}\)

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Question 4 of 50

Question 4

Easy

Given that an observation is in the Bus row, what is the probability it is also On time?

Selected condition: Given Bus: the entire row is the denominator; the On time cell is the numerator.

Commute method and arrival status
Commute method / Arrival status	On time	Late	Total
Bus	36	9	45
Walk	28	4	32
Bicycle	22	6	28
Total	86	19	105

\(\frac{12}{35}\)\(\frac{18}{43}\)\(\frac{3}{7}\)\(\frac{4}{5}\)

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Question 5 of 50

Question 5

Easy

What percentage of all observations are both Bus and On time?

Commute method and arrival status
Commute method / Arrival status	On time	Late	Total
Bus	36	9	45
Walk	28	4	32
Bicycle	22	6	28
Total	86	19	105

\(34.3\%\)\(80\%\)\(42.9\%\)\(81.9\%\)

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Question 6 of 50

Question 6

Easy

According to the displayed table, what is the total number in the In person row?

Selected condition: Use the In person row.

Workshop format and certification result
Workshop format / Certification result	Certified	Not certified	Total
Online	44	16	60
In person	51	9	60
Total	95	25	120

\(9\)\(60\)\(25\)\(120\)

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Question 7 of 50

Question 7

Easy

According to the displayed table, what is the total number in the Not certified column?

Selected condition: Use the Not certified column.

Workshop format and certification result
Workshop format / Certification result	Certified	Not certified	Total
Online	44	16	60
In person	51	9	60
Total	95	25	120

\(9\)\(60\)\(25\)\(120\)

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Question 8 of 50

Question 8

Easy

If one observation is selected from the full table, what is the probability it is both In person AND Not certified?

Selected condition: In person AND Not certified: use the labeled intersection cell.

Workshop format and certification result
Workshop format / Certification result	Certified	Not certified	Total
Online	44	16	60
In person	51	9	60
Total	95	25	120

\(\frac{3}{20}\)\(\frac{9}{25}\)\(\frac{1}{2}\)\(\frac{3}{40}\)

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Question 9 of 50

Question 9

Easy

Given that an observation is in the In person row, what is the probability it is also Not certified?

Selected condition: Given In person: the entire row is the denominator; the Not certified cell is the numerator.

Workshop format and certification result
Workshop format / Certification result	Certified	Not certified	Total
Online	44	16	60
In person	51	9	60
Total	95	25	120

\(\frac{3}{20}\)\(\frac{3}{40}\)\(\frac{9}{25}\)\(\frac{1}{2}\)

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Question 10 of 50

Question 10

Easy

Within the In person row, what percentage are Not certified?

Selected condition: Within In person: use that row total.

Workshop format and certification result
Workshop format / Certification result	Certified	Not certified	Total
Online	44	16	60
In person	51	9	60
Total	95	25	120

\(7.5\%\)\(15\%\)\(50\%\)\(36\%\)

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Question 11 of 50

Question 11

Easy

According to the displayed table, what is the total number in the Laptop row?

Selected condition: Use the Laptop row.

Primary device and notification setting
Primary device / Notifications	Enabled	Disabled	Total
Phone	54	18	72
Tablet	23	17	40
Laptop	41	27	68
Total	118	62	180

\(41\)\(118\)\(68\)\(180\)

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Question 12 of 50

Question 12

Easy

According to the displayed table, what is the total number in the Enabled column?

Selected condition: Use the Enabled column.

Primary device and notification setting
Primary device / Notifications	Enabled	Disabled	Total
Phone	54	18	72
Tablet	23	17	40
Laptop	41	27	68
Total	118	62	180

\(41\)\(68\)\(180\)\(118\)

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Question 13 of 50

Question 13

Easy

If one observation is selected from the full table, what is the probability it is both Laptop AND Enabled?

Selected condition: Laptop AND Enabled: use the labeled intersection cell.

Primary device and notification setting
Primary device / Notifications	Enabled	Disabled	Total
Phone	54	18	72
Tablet	23	17	40
Laptop	41	27	68
Total	118	62	180

\(\frac{41}{180}\)\(\frac{41}{68}\)\(\frac{41}{118}\)\(\frac{17}{45}\)

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Question 14 of 50

Question 14

Easy

Given that an observation is in the Laptop row, what is the probability it is also Enabled?

Selected condition: Given Laptop: the entire row is the denominator; the Enabled cell is the numerator.

Primary device and notification setting
Primary device / Notifications	Enabled	Disabled	Total
Phone	54	18	72
Tablet	23	17	40
Laptop	41	27	68
Total	118	62	180

\(\frac{41}{180}\)\(\frac{41}{68}\)\(\frac{41}{118}\)\(\frac{17}{45}\)

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Question 15 of 50

Question 15

Easy

The Laptop row total is \(68\). If the Enabled cell were hidden, what value would complete the row?

Selected condition: Use the Laptop row total and its known cells.

Primary device and notification setting
Primary device / Notifications	Enabled	Disabled	Total
Phone	54	18	72
Tablet	23	17	40
Laptop	41	27	68
Total	118	62	180

\(68\)\(118\)\(41\)\(27\)

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Question 16 of 50

Question 16

Medium

According to the displayed table, what is the total number in the Morning row?

Selected condition: Use the Morning row.

Library visit period and checkout status
Visit period / Checkout status	Checked out item	No checkout	Total
Morning	29	11	40
Afternoon	48	12	60
Evening	33	17	50
Total	110	40	150

\(11\)\(150\)\(0\)\(40\)

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Question 17 of 50

Question 17

Medium

According to the displayed table, what is the total number in the No checkout column?

Selected condition: Use the No checkout column.

Library visit period and checkout status
Visit period / Checkout status	Checked out item	No checkout	Total
Morning	29	11	40
Afternoon	48	12	60
Evening	33	17	50
Total	110	40	150

\(40\)\(11\)\(150\)\(0\)

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Question 18 of 50

Question 18

Medium

If one observation is selected from the full table, what is the probability it is both Morning AND No checkout?

Selected condition: Morning AND No checkout: use the labeled intersection cell.

Library visit period and checkout status
Visit period / Checkout status	Checked out item	No checkout	Total
Morning	29	11	40
Afternoon	48	12	60
Evening	33	17	50
Total	110	40	150

\(\frac{11}{40}\)\(\frac{11}{150}\)\(\frac{4}{15}\)\(0\)

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Question 19 of 50

Question 19

Medium

Given that an observation is in the Morning row, what is the probability it is also No checkout?

Selected condition: Given Morning: the entire row is the denominator; the No checkout cell is the numerator.

Library visit period and checkout status
Visit period / Checkout status	Checked out item	No checkout	Total
Morning	29	11	40
Afternoon	48	12	60
Evening	33	17	50
Total	110	40	150

\(\frac{11}{150}\)\(\frac{4}{15}\)\(\frac{11}{40}\)\(0\)

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Question 20 of 50

Question 20

Medium

If the No checkout column total were missing, what value would make the column totals sum to the grand total?

Library visit period and checkout status
Visit period / Checkout status	Checked out item	No checkout	Total
Morning	29	11	40
Afternoon	48	12	60
Evening	33	17	50
Total	110	40	150

\(150\)\(110\)\(0\)\(40\)

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Question 21 of 50

Question 21

Medium

According to the displayed table, what is the total number in the Guided row?

Selected condition: Use the Guided row.

Training plan and skills assessment
Training plan / Assessment result	Passed	Needs review	Total
Guided	63	12	75
Independent	42	18	60
Total	105	30	135

\(75\)\(63\)\(105\)\(135\)

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Question 22 of 50

Question 22

Medium

According to the displayed table, what is the total number in the Passed column?

Selected condition: Use the Passed column.

Training plan and skills assessment
Training plan / Assessment result	Passed	Needs review	Total
Guided	63	12	75
Independent	42	18	60
Total	105	30	135

\(63\)\(105\)\(75\)\(135\)

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Question 23 of 50

Question 23

Medium

If one observation is selected from the full table, what is the probability it is both Guided AND Passed?

Selected condition: Guided AND Passed: use the labeled intersection cell.

Training plan and skills assessment
Training plan / Assessment result	Passed	Needs review	Total
Guided	63	12	75
Independent	42	18	60
Total	105	30	135

\(\frac{21}{25}\)\(\frac{3}{5}\)\(\frac{7}{15}\)\(\frac{5}{9}\)

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Question 24 of 50

Question 24

Medium

Given that an observation is in the Guided row, what is the probability it is also Passed?

Selected condition: Given Guided: the entire row is the denominator; the Passed cell is the numerator.

Training plan and skills assessment
Training plan / Assessment result	Passed	Needs review	Total
Guided	63	12	75
Independent	42	18	60
Total	105	30	135

\(\frac{7}{15}\)\(\frac{3}{5}\)\(\frac{5}{9}\)\(\frac{21}{25}\)

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Question 25 of 50

Question 25

Medium

By approximately how many percentage points do the Passed conditional rates differ between the two rows?

Training plan and skills assessment
Training plan / Assessment result	Passed	Needs review	Total
Guided	63	12	75
Independent	42	18	60
Total	105	30	135

\(14.0\text{ percentage points}\)\(21\text{ points}\)\(0.14\%\)\(46.7\%\)

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Question 26 of 50

Question 26

Medium

According to the displayed table, what is the total number in the Service row?

Selected condition: Use the Service row.

Club type and student year
Club type / Student year	Junior	Senior	Total
Arts	24	31	55
Robotics	37	28	65
Service	29	41	70
Total	90	100	190

\(41\)\(70\)\(100\)\(190\)

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Question 27 of 50

Question 27

Medium

According to the displayed table, what is the total number in the Senior column?

Selected condition: Use the Senior column.

Club type and student year
Club type / Student year	Junior	Senior	Total
Arts	24	31	55
Robotics	37	28	65
Service	29	41	70
Total	90	100	190

\(41\)\(70\)\(100\)\(190\)

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Question 28 of 50

Question 28

Medium

If one observation is selected from the full table, what is the probability it is both Service AND Senior?

Selected condition: Service AND Senior: use the labeled intersection cell.

Club type and student year
Club type / Student year	Junior	Senior	Total
Arts	24	31	55
Robotics	37	28	65
Service	29	41	70
Total	90	100	190

\(\frac{41}{70}\)\(\frac{41}{100}\)\(\frac{7}{19}\)\(\frac{41}{190}\)

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Question 29 of 50

Question 29

Medium

Given that an observation is in the Service row, what is the probability it is also Senior?

Selected condition: Given Service: the entire row is the denominator; the Senior cell is the numerator.

Club type and student year
Club type / Student year	Junior	Senior	Total
Arts	24	31	55
Robotics	37	28	65
Service	29	41	70
Total	90	100	190

\(\frac{41}{70}\)\(\frac{41}{190}\)\(\frac{41}{100}\)\(\frac{7}{19}\)

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Question 30 of 50

Question 30

Medium

Given that an observation is Senior, what is the probability it belongs to the Service row?

Selected condition: Given Senior: use the column total, not the Service row total.

Club type and student year
Club type / Student year	Junior	Senior	Total
Arts	24	31	55
Robotics	37	28	65
Service	29	41	70
Total	90	100	190

\(\frac{41}{70}\)\(\frac{41}{100}\)\(\frac{41}{190}\)\(\frac{10}{19}\)

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Question 31 of 50

Question 31

Medium

According to the displayed table, what is the total number in the Weekday row?

Selected condition: Use the Weekday row.

Study schedule and session attendance
Study schedule / Attendance	Attended	Absent	Total
Weekday	72	18	90
Weekend	46	14	60
Total	118	32	150

\(72\)\(118\)\(90\)\(150\)

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Question 32 of 50

Question 32

Medium

According to the displayed table, what is the total number in the Attended column?

Selected condition: Use the Attended column.

Study schedule and session attendance
Study schedule / Attendance	Attended	Absent	Total
Weekday	72	18	90
Weekend	46	14	60
Total	118	32	150

\(72\)\(90\)\(150\)\(118\)

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Question 33 of 50

Question 33

Medium

If one observation is selected from the full table, what is the probability it is both Weekday AND Attended?

Selected condition: Weekday AND Attended: use the labeled intersection cell.

Study schedule and session attendance
Study schedule / Attendance	Attended	Absent	Total
Weekday	72	18	90
Weekend	46	14	60
Total	118	32	150

\(\frac{12}{25}\)\(\frac{4}{5}\)\(\frac{36}{59}\)\(\frac{3}{5}\)

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Question 34 of 50

Question 34

Medium

Given that an observation is in the Weekday row, what is the probability it is also Attended?

Selected condition: Given Weekday: the entire row is the denominator; the Attended cell is the numerator.

Study schedule and session attendance
Study schedule / Attendance	Attended	Absent	Total
Weekday	72	18	90
Weekend	46	14	60
Total	118	32	150

\(\frac{12}{25}\)\(\frac{4}{5}\)\(\frac{36}{59}\)\(\frac{3}{5}\)

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Question 35 of 50

Question 35

Medium

For \(P(Attended\midWeekday)\), which table count must be the denominator?

Selected condition: The condition is Weekday.

Study schedule and session attendance
Study schedule / Attendance	Attended	Absent	Total
Weekday	72	18	90
Weekend	46	14	60
Total	118	32	150

\(150\)\(118\)\(90\)\(72\)

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Question 36 of 50

Question 36

Medium

According to the displayed table, what is the total number in the Middle row?

Selected condition: Use the Middle row.

Volunteer shift and task completion
Volunteer shift / Task status	Completed	Incomplete	Total
Early	38	7	45
Middle	44	11	55
Late	27	13	40
Total	109	31	140

\(11\)\(31\)\(140\)\(55\)

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Question 37 of 50

Question 37

Medium

According to the displayed table, what is the total number in the Incomplete column?

Selected condition: Use the Incomplete column.

Volunteer shift and task completion
Volunteer shift / Task status	Completed	Incomplete	Total
Early	38	7	45
Middle	44	11	55
Late	27	13	40
Total	109	31	140

\(31\)\(11\)\(55\)\(140\)

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Question 38 of 50

Question 38

Medium

If one observation is selected from the full table, what is the probability it is both Middle AND Incomplete?

Selected condition: Middle AND Incomplete: use the labeled intersection cell.

Volunteer shift and task completion
Volunteer shift / Task status	Completed	Incomplete	Total
Early	38	7	45
Middle	44	11	55
Late	27	13	40
Total	109	31	140

\(\frac{1}{5}\)\(\frac{11}{140}\)\(\frac{11}{31}\)\(\frac{11}{28}\)

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Question 39 of 50

Question 39

Medium

Given that an observation is in the Middle row, what is the probability it is also Incomplete?

Selected condition: Given Middle: the entire row is the denominator; the Incomplete cell is the numerator.

Volunteer shift and task completion
Volunteer shift / Task status	Completed	Incomplete	Total
Early	38	7	45
Middle	44	11	55
Late	27	13	40
Total	109	31	140

\(\frac{11}{140}\)\(\frac{11}{31}\)\(\frac{1}{5}\)\(\frac{11}{28}\)

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Question 40 of 50

Question 40

Medium

What is the grand total obtained by summing all row totals?

Volunteer shift and task completion
Volunteer shift / Task status	Completed	Incomplete	Total
Early	38	7	45
Middle	44	11	55
Late	27	13	40
Total	109	31	140

\(45\)\(109\)\(280\)\(140\)

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Question 41 of 50

Question 41

Hard

According to the displayed table, what is the total number in the Hybrid row?

Selected condition: Use the Hybrid row.

Course format and project submission
Course format / Project submission	Submitted	Missing	Total
Hybrid	58	12	70
Classroom	66	14	80
Total	124	26	150

\(70\)\(58\)\(124\)\(150\)

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Question 42 of 50

Question 42

Hard

According to the displayed table, what is the total number in the Submitted column?

Selected condition: Use the Submitted column.

Course format and project submission
Course format / Project submission	Submitted	Missing	Total
Hybrid	58	12	70
Classroom	66	14	80
Total	124	26	150

\(58\)\(124\)\(70\)\(150\)

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Question 43 of 50

Question 43

Hard

If one observation is selected from the full table, what is the probability it is both Hybrid AND Submitted?

Selected condition: Hybrid AND Submitted: use the labeled intersection cell.

Course format and project submission
Course format / Project submission	Submitted	Missing	Total
Hybrid	58	12	70
Classroom	66	14	80
Total	124	26	150

\(\frac{29}{35}\)\(\frac{29}{62}\)\(\frac{29}{75}\)\(\frac{7}{15}\)

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Question 44 of 50

Question 44

Hard

Given that an observation is in the Hybrid row, what is the probability it is also Submitted?

Selected condition: Given Hybrid: the entire row is the denominator; the Submitted cell is the numerator.

Course format and project submission
Course format / Project submission	Submitted	Missing	Total
Hybrid	58	12	70
Classroom	66	14	80
Total	124	26	150

\(\frac{29}{75}\)\(\frac{29}{62}\)\(\frac{7}{15}\)\(\frac{29}{35}\)

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Question 45 of 50

Question 45

Hard

What is the marginal probability that an observation belongs to the Hybrid row?

Selected condition: Use the Hybrid row total.

Course format and project submission
Course format / Project submission	Submitted	Missing	Total
Hybrid	58	12	70
Classroom	66	14	80
Total	124	26	150

\(\frac{7}{15}\)\(\frac{29}{75}\)\(\frac{29}{35}\)\(\frac{62}{75}\)

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Question 46 of 50

Question 46

Hard

According to the displayed table, what is the total number in the Swimming row?

Selected condition: Use the Swimming row.

Recreation choice and membership type
Recreation choice / Membership type	Monthly	Annual	Total
Swimming	21	34	55
Climbing	26	29	55
Running	32	38	70
Total	79	101	180

\(34\)\(55\)\(101\)\(180\)

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Question 47 of 50

Question 47

Hard

According to the displayed table, what is the total number in the Annual column?

Selected condition: Use the Annual column.

Recreation choice and membership type
Recreation choice / Membership type	Monthly	Annual	Total
Swimming	21	34	55
Climbing	26	29	55
Running	32	38	70
Total	79	101	180

\(34\)\(55\)\(101\)\(180\)

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Question 48 of 50

Question 48

Hard

If one observation is selected from the full table, what is the probability it is both Swimming AND Annual?

Selected condition: Swimming AND Annual: use the labeled intersection cell.

Recreation choice and membership type
Recreation choice / Membership type	Monthly	Annual	Total
Swimming	21	34	55
Climbing	26	29	55
Running	32	38	70
Total	79	101	180

\(\frac{34}{55}\)\(\frac{34}{101}\)\(\frac{11}{36}\)\(\frac{17}{90}\)

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Question 49 of 50

Question 49

Hard

Given that an observation is in the Swimming row, what is the probability it is also Annual?

Selected condition: Given Swimming: the entire row is the denominator; the Annual cell is the numerator.

Recreation choice and membership type
Recreation choice / Membership type	Monthly	Annual	Total
Swimming	21	34	55
Climbing	26	29	55
Running	32	38	70
Total	79	101	180

\(\frac{34}{55}\)\(\frac{17}{90}\)\(\frac{34}{101}\)\(\frac{11}{36}\)

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Question 50 of 50

Question 50

Hard

What conditional percentage of the Swimming group is Annual?

Selected condition: Restrict to Swimming; then use the Annual cell.

Recreation choice and membership type
Recreation choice / Membership type	Monthly	Annual	Total
Swimming	21	34	55
Climbing	26	29	55
Running	32	38	70
Total	79	101	180

\(18.9\%\)\(61.8\%\)\(56.1\%\)\(30.6\%\)

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Practice complete

Your practice summary

Use the results to decide what to review before your next attempt.

Score0 / 500% accuracy

Correct: 0
Incorrect: 0
Completed: 50 / 50

Questions to review

Question 1Read row totals
Easy
Question 2Read column totals
Easy
Question 3Joint probability
Easy
Question 4Conditional probability from a row
Easy
Question 5Overall relative frequency
Easy
Question 6Read row totals
Easy
Question 7Read column totals
Easy
Question 8Joint probability
Easy
Question 9Conditional probability from a row
Easy
Question 10Conditional relative frequency
Easy
Question 11Read row totals
Easy
Question 12Read column totals
Easy
Question 13Joint probability
Easy
Question 14Conditional probability from a row
Easy
Question 15Find a missing table cell
Easy
Question 16Read row totals
Medium
Question 17Read column totals
Medium
Question 18Joint probability
Medium
Question 19Conditional probability from a row
Medium
Question 20Find a missing marginal total
Medium
Question 21Read row totals
Medium
Question 22Read column totals
Medium
Question 23Joint probability
Medium
Question 24Conditional probability from a row
Medium
Question 25Compare conditional rates
Medium
Question 26Read row totals
Medium
Question 27Read column totals
Medium
Question 28Joint probability
Medium
Question 29Conditional probability from a row
Medium
Question 30Reverse conditional probability
Medium
Question 31Read row totals
Medium
Question 32Read column totals
Medium
Question 33Joint probability
Medium
Question 34Conditional probability from a row
Medium
Question 35Identify conditional denominator
Medium
Question 36Read row totals
Medium
Question 37Read column totals
Medium
Question 38Joint probability
Medium
Question 39Conditional probability from a row
Medium
Question 40Validate grand totals
Medium
Question 41Read row totals
Hard
Question 42Read column totals
Hard
Question 43Joint probability
Hard
Question 44Conditional probability from a row
Hard
Question 45Marginal probability
Hard
Question 46Read row totals
Hard
Question 47Read column totals
Hard
Question 48Joint probability
Hard
Question 49Conditional probability from a row
Hard
Question 50Conditional percentage
Hard

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