Relative Risk vs Odds Ratio Flashcards: Two-Way Table Practice

Question 1

A fictional batch contains 7 scratched panels and 21 unscratched panels. For a uniformly selected panel from this batch, what is the probability of a scratch?

Accepted Answer

1/4 (25%)

Probability uses all 28 panels: 7 ÷ (7 + 21).

Question 2

In a fictional inspection record, the relative risk of a dent is 7/4 for Press A compared with Press B. Express this as a probability multiplier.

Accepted Answer

Press A’s recorded dent probability is 7/4 (1.75) times Press B’s.

The ratio compares event probabilities, with Press B as the reference.

Question 3

In a fictional record, the scratch proportion is 15% for Belt A and 10% for Belt B. A learner says RR = 1.5 means A is 50 percentage points higher. What is the correct percentage-point difference?

Accepted Answer

5 percentage points

15% − 10% = 5 percentage points. The 50% increase is relative to B’s 10% baseline.

Question 4

Fictional inspection counts:

Line | Cracked | Not cracked
Cedar | 9 | 51
Maple | 6 | 74

For a crack, what is the relative risk (risk ratio), Cedar compared with Maple?

Accepted Answer

2

RR = (9/60) ÷ (6/80) = (3/20) ÷ (3/40). Cedar’s observed crack proportion is twice Maple’s.

Question 5

A fictional batch contains 8 misprinted labels and 24 correctly printed labels. What are the odds of a misprint versus a correct print within this batch?

Accepted Answer

1/3

Odds use event count ÷ other-outcome count: 8/24. The probability would instead be 8/32.

Question 6

Fictional inspection counts:

Workshop | Rework needed | No rework
East | 12 | 48
West | 5 | 50

For rework versus no rework, what is the odds ratio, East compared with West?

Accepted Answer

5/2 (2.5)

OR = (12/48) ÷ (5/50) = (1/4) ÷ (1/10).

Question 7

For fictional Lines A and B, the recorded odds ratio for a reject is 4, A compared with B. A learner says this alone means A’s reject probability is four times B’s. Is that interpretation valid?

Accepted Answer

No. The reject odds are four times as large.

An odds multiplier is not generally a probability multiplier; the baseline probability is needed to translate it.

Question 8

Fictional counts: Scanner A flags 18 of 90 items; Scanner B flags 12 of 30. A learner divides 18 by 12 to compare flag probabilities. What is the correct risk ratio, A compared with B?

Accepted Answer

1/2 (0.5)

Use within-scanner proportions: (18/90) ÷ (12/30) = (1/5) ÷ (2/5). Raw flag counts ignore unequal totals.

Question 9

A fictional bin holds 11 chipped tiles and 44 unchipped tiles. A learner calls 11/55 the odds of a chip versus no chip. What is the corrected odds value?

Accepted Answer

1/4

Use 11/44 for odds. The value 11/55 is the chip probability.

Question 10

Fictional inspection counts:

Batch | Smooth | Rough
Copper | 54 | 18
Silver | 42 | 7

For rough versus smooth, what is the odds ratio, Copper compared with Silver?

Accepted Answer

2

OR = (18/54) ÷ (7/42) = (1/3) ÷ (1/6). Read the outcome labels before forming the ratio.

Question 11

The recorded relative risk of a barcode error is 2/5 for Printer A compared with Printer B. By what percent is A’s error probability lower?

Accepted Answer

60% lower

1 − 2/5 = 3/5 = 60%, relative to Printer B’s error probability.

Question 12

Fictional counts: Machine A produces 14 rejects among 70 items; Machine B produces 5 rejects among 50. For a reject, what is the risk ratio, B compared with A?

Accepted Answer

1/2

RR = (5/50) ÷ (14/70) = (1/10) ÷ (1/5). B is the numerator group; A is the reference.

Question 13

A fictional record has RR = 1 for a dent, Group A compared with Group B, and B’s dent probability is positive. What is equal between the groups?

Accepted Answer

Their recorded dent probabilities.

A ratio of 1 means the numerator and denominator probabilities are equal. It does not require equal group sizes or dent counts.

Question 14

Fictional inspection counts:

Depot | Delayed | On time
North | 4 | 20
South | 9 | 45

For delay versus on-time arrival, what is the odds ratio, North compared with South?

Accepted Answer

1

OR = (4/20) ÷ (9/45) = (1/5) ÷ (1/5). Different counts can give equal odds.

Question 15

The recorded risk ratio for a late delivery is 9/8 for Depot A compared with Depot B. By what percent is A’s late-delivery probability higher?

Accepted Answer

12.5% higher

(9/8 − 1) × 100% = (1/8) × 100%, relative to Depot B.

Question 16

Fictional inspection counts:

Outcome | Robot Red | Robot Blue
Misaligned | 6 | 15
Aligned | 54 | 60

For misalignment, what is the risk ratio, Red compared with Blue?

Accepted Answer

1/2 (0.5)

RR = (6/60) ÷ (15/75) = (1/10) ÷ (1/5). Each robot’s column supplies its own total.

Question 17

For fictional Groups A and B, the odds of a faulty item versus a sound item are 2/3 and 1/4, respectively. What is the odds ratio for sound versus faulty, A compared with B?

Accepted Answer

3/8

Complementing the event inverts each odds: (3/2) ÷ 4 = 3/8.

Question 18

Fictional inspection counts:

Group | Bent | Straight
B | 9 | 45
A | 12 | 30

For bent versus straight, what is the odds ratio, B compared with A?

Accepted Answer

1/2

OR = (9/45) ÷ (12/30) = (1/5) ÷ (2/5). The requested comparison starts with B.

Question 19

Exact two-group exercise: Group B’s event probability is 1/4. The unadjusted event odds ratio is 3, Group A compared with B. What is A’s event probability?

Accepted Answer

1/2

B’s odds = (1/4)/(3/4) = 1/3. A’s odds = 3 × 1/3 = 1, so A’s probability = 1/(1 + 1).

Question 20

Fictional inspection counts:

Route | Damaged | Undamaged
Hill | 5 | 20
Lake | 12 | 48

For damage, what is the risk ratio, Hill compared with Lake?

Accepted Answer

1

RR = (5/25) ÷ (12/60) = (1/5) ÷ (1/5). The event proportions are equal.

Question 21

In a fictional record, defect probabilities are 1/5 for Group A and 1/10 for Group B. What is the risk ratio for being defect-free, A compared with B?

Accepted Answer

8/9

The complement probabilities are 4/5 and 9/10. Their ratio is (4/5) ÷ (9/10) = 8/9.

Question 22

Fictional inspection counts:

Station | Loose | Tight
Birch | 6 | 42
Elm | 15 | 35

For loose versus tight, what is the odds ratio, Birch compared with Elm?

Accepted Answer

1/3

OR = (6/42) ÷ (15/35) = (1/7) ÷ (3/7).

Question 23

For a fixed event, RR for Group A compared with Group B is 0: A’s event probability is 0 and B’s is positive. Does reversing the reference group give a finite risk ratio?

Accepted Answer

No. The reversed risk ratio is undefined as a finite real number.

It would divide B’s positive probability by A’s zero probability; 1/0 is not a finite value.

Question 24

Exact two-group exercise: Group B’s event probability is 1/2. The unadjusted event odds ratio is 3, Group A compared with B. What is A’s event probability?

Accepted Answer

3/4

B’s odds are 1. A’s odds are 3, so A’s probability is 3/(1 + 3).

Question 25

In a fictional record, pass probabilities are 3/4 for Group A and 1/2 for Group B. A learner says the failure risk ratio, A compared with B, is the reciprocal of the pass risk ratio. What is the correct failure risk ratio?

Accepted Answer

1/2

Failure probabilities are 1/4 and 1/2: (1/4) ÷ (1/2) = 1/2. Complementing the outcome does not generally reciprocate an RR.

Question 26

In a fictional record, the odds ratio for a machine flag is 7/4 for Group A compared with Group B. By what percent are A’s flag odds higher?

Accepted Answer

75% higher odds

(7/4 − 1) × 100% = 75%. This is an odds comparison, not a percentage-point difference or a probability multiplier.

Question 27

Exact fictional event probabilities are 3/400 in Group A and 1/400 in Group B. What is the odds ratio, A compared with B?

Accepted Answer

1197/397 (about 3.0151)

OR = (3/397) ÷ (1/399). RR = 3 is close here because both event probabilities are small; this gives no universal cutoff.

Question 28

Fictional counts: Group A has 0 faulty and 16 sound items; Group B has 3 faulty and 12 sound items. For faulty versus sound, what is the odds ratio, A compared with B?

Accepted Answer

0

A’s odds are 0/16 = 0; B’s are 3/12 = 1/4. Thus OR = 0 ÷ (1/4).

Question 29

Exact two-group exercise: the event probability in Group B is 3/20, and RR is 2 for Group A compared with B. What is A’s event probability?

Accepted Answer

3/10 (30%)

Multiply the reference probability by RR: 2 × 3/20.

Question 30

Both groups have event probabilities strictly between 0 and 1. The event odds ratio is 5/3 for Group A compared with B. What is the non-event odds ratio for the same group comparison?

Accepted Answer

3/5

Complementing the event reciprocates each within-group odds, so it reciprocates their ratio. The stated probability bounds keep both ratios finite and nonzero.

Question 31

Fictional counts:

Group | Acceptable | Rejected
A | 24 | 8
B | 45 | 5

A learner uses (24 × 5)/(8 × 45) for rejected-versus-acceptable odds, A compared with B. What is the corrected odds ratio?

Accepted Answer

3

Use (8/24) ÷ (5/45) = (8 × 45)/(24 × 5) = 3. The proposed product gives the reverse comparison.

Question 32

A fictional audit records every item produced by two existing lines during the same week. Line A has twice Line B’s reject proportion. Does this alone establish that using Line A causes a higher reject probability?

Accepted Answer

No. The record establishes an association for that week.

The lines may also differ in materials or other conditions. Complete recording does not remove confounding.

Question 33

Fictional counts: Group A has 4 damaged items out of 20; Group B has 0 damaged out of 15. For damage, is the risk ratio A compared with B a finite real number?

Accepted Answer

No. It is undefined as a finite real number.

The calculation is (4/20) ÷ (0/15) = (1/5) ÷ 0.

Question 34

An exact two-group comparison gives an event odds ratio of 2 for A compared with B, but gives no baseline probability. Can A’s event probability be determined uniquely?

Accepted Answer

No. A baseline probability is also needed.

If B’s probability is 1/3, A’s is 1/2; if B’s is 1/2, A’s is 2/3. Both pairs give OR = 2.

Question 35

Exact fictional event probabilities are 9/16 in Group A and 3/16 in Group B. What is the odds ratio, A compared with B?

Accepted Answer

39/7 (about 5.5714)

OR = (9/7) ÷ (3/13) = 39/7. RR = 3, so treating OR as RR would give a substantial error here.

Question 36

Fictional counts:

Group | Returned | Kept
A | 6 | 24
B | 4 | 36

A learner divides (6/70) by (4/70). What is the correct risk ratio for a return, A compared with B?

Accepted Answer

2

Use each group’s total: (6/30) ÷ (4/40) = (1/5) ÷ (1/10). The grand total of 70 is not either conditional denominator.

Question 37

Fictional counts: Group A has 10 flagged and 0 unflagged items; Group B has 5 flagged and 15 unflagged. For flagged versus unflagged, does ordinary division give a finite odds ratio, A compared with B?

Accepted Answer

No. A’s within-group odds already require division by zero.

A’s odds would be 10/0. Do not report a finite OR or silently add counts to the table.

Question 38

Exact two-group exercise: Group B’s event probability is 3/5. Can the event risk ratio be 2 for Group A compared with B?

Accepted Answer

No. It would require an impossible probability.

A’s probability would be 2 × 3/5 = 6/5, which exceeds 1.

Question 39

A fictional archive deliberately selects 40 failed items and 40 passing items, then records each item’s production line. Can within-line failure proportions in this selected table alone establish the source population’s failure risk ratio?

Accepted Answer

No. Outcome-selected counts alone do not establish the population risk ratio.

Selection fixed the failed-versus-passing mix. Population risks require further information about the sampling fractions or source counts.

Question 40

In a fictional record, the odds ratio for a failed seal is 3/5 for Method A compared with Method B. By what percent are A’s failed-seal odds lower?

Accepted Answer

40% lower odds

1 − 3/5 = 2/5 = 40%. This does not say the failure probability is 40% lower.

Question 41

Fictional counts: Group A has 0 late orders out of 18; Group B has 2 late orders out of 24. For lateness, what is the risk ratio, A compared with B?

Accepted Answer

0

RR = (0/18) ÷ (2/24) = 0 ÷ (1/12). A zero numerator is allowed when the reference probability is positive.

Question 42

Exact two-group exercise: Group B’s event probability is 1/3. The unadjusted event odds ratio is 4, Group A compared with B. What is A’s event probability?

Accepted Answer

2/3

B’s odds are (1/3)/(2/3) = 1/2. A’s odds are 4 × 1/2 = 2, giving probability 2/(1 + 2).

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Relative Risk vs Odds Ratio Flashcards: Two-Way Table Practice