Probability and Two-Way Tables · Sub-skill drill
Probability from Two-Way Tables
Two-way tables organize data by two categorical variables. Each cell counts the number of items in the intersection of one category from each variable. Reading these tables for SAT probability questions requires care: 'probability of A given B' uses only the row or column for B as the denominator, not the grand total. Circle the conditioning category before computing. The College Board lists both the conditional probability and the unconditional probability as answer choices, so the difference matters.
How this sub-skill is tested on the SAT
Two-way tables organize data by two categorical variables. Each cell counts the number of items in the intersection of one category from each variable. Reading these tables for SAT probability questions requires care: 'probability of A given B' uses only the row or column for B as the denominator, not the grand total. Circle the conditioning category before computing. The College Board lists both the conditional probability and the unconditional probability as answer choices, so the difference matters.
This sub-skill sits inside the broader Probability and Two-Way Tables topic, which is part of the College Board's Problem Solving & Data Analysis content domain. Problem Solving and Data Analysis is where the SAT pretends to be the real world. Every question in this domain is wrapped in context: a recipe, a survey, a clinical trial, a lab measurement, a marketing report. The math itself is rarely harder than middle-school arithmetic — ratios, proportions, percentages, unit conversions, means, medians, scatter plots, two-way tables, and basic probability. What trips students up is the reading. The College Board has spent two decades calibrating these prompts to reward students who slow down on the setup and punish students who rush to compute. ScoreRe
Practice questions in this drill set
Below are 6 practice questions targeting this exact sub-skill, ordered from easier to harder. Each question is tagged with its target score band so you can focus on questions that match the band you are working out of. Worked solutions are open by default — read each one even if you got the question right, because the way the solution is structured often reveals a faster path than the one you used.
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A school surveyed students about a proposed schedule change. 46 boys and 59 girls said yes; 49 boys and 55 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?
- A 59/105
- B 46/105
- C 46/209
- D 105/209
Worked solution
Answer: B — 46/105
Conditional probability uses only the subset that said yes as the denominator. That subset is 46 + 59 = 105. Boys in that subset = 46. Probability = 46/105 = 46/105.
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A school surveyed students about a proposed schedule change. 28 boys and 70 girls said yes; 21 boys and 70 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?
- A 2/7
- B 5/7
- C 14/27
- D 4/27
Worked solution
Answer: A — 2/7
Conditional probability uses only the subset that said yes as the denominator. That subset is 28 + 70 = 98. Boys in that subset = 28. Probability = 28/98 = 2/7.
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A school surveyed students about a proposed schedule change. 41 boys and 38 girls said yes; 47 boys and 41 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?
- A 38/79
- B 41/167
- C 79/167
- D 41/79
Worked solution
Answer: D — 41/79
Conditional probability uses only the subset that said yes as the denominator. That subset is 41 + 38 = 79. Boys in that subset = 41. Probability = 41/79 = 41/79.
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A school surveyed students about a proposed schedule change. 70 boys and 20 girls said yes; 79 boys and 79 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?
- A 35/124
- B 2/9
- C 7/9
- D 45/124
Worked solution
Answer: C — 7/9
Conditional probability uses only the subset that said yes as the denominator. That subset is 70 + 20 = 90. Boys in that subset = 70. Probability = 70/90 = 7/9.
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A school surveyed students about a proposed schedule change. 74 boys and 60 girls said yes; 72 boys and 35 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?
- A 74/241
- B 134/241
- C 37/67
- D 30/67
Worked solution
Answer: C — 37/67
Conditional probability uses only the subset that said yes as the denominator. That subset is 74 + 60 = 134. Boys in that subset = 74. Probability = 74/134 = 37/67.
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A school surveyed students about a proposed schedule change. 55 boys and 42 girls said yes; 48 boys and 24 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?
- A 42/97
- B 97/169
- C 55/97
- D 55/169
Worked solution
Answer: C — 55/97
Conditional probability uses only the subset that said yes as the denominator. That subset is 55 + 42 = 97. Boys in that subset = 55. Probability = 55/97 = 55/97.
Why this band assignment matters
Every question in this drill is tagged with a target score band — 400–500, 500–600, 600–700, or 700–800 — based on its difficulty and the patterns the College Board uses for questions at each level. If you are aiming to break out of a 580 plateau, the 600–700 questions in this drill are your highest-leverage practice. If you are chasing 750+, the 700–800 questions here are the ones that separate the top 10% of test takers from everyone else.
Use the band tags to filter your work. If you can confidently solve every 400–500 and 500–600 question without notes, move to the 600–700 set. If those land cleanly, the 700–800 set is your final boss. The worked solutions in this drill are written so that even the hardest questions become learnable patterns once you have seen the structure of the solve a few times.