Probability and Two-Way Tables · Sub-skill drill
Simple Probability
Simple probability is the number of favorable outcomes divided by the total number of equally likely outcomes. SAT simple-probability questions usually present a sample of objects, people, or events and ask for the probability of selecting one with a particular property. The arithmetic is straightforward; the difficulty is identifying the correct denominator. Students who use the wrong total — for example, the count of one row instead of the grand total — get answers that match listed wrong-answer choices.
How this sub-skill is tested on the SAT
Simple probability is the number of favorable outcomes divided by the total number of equally likely outcomes. SAT simple-probability questions usually present a sample of objects, people, or events and ask for the probability of selecting one with a particular property. The arithmetic is straightforward; the difficulty is identifying the correct denominator. Students who use the wrong total — for example, the count of one row instead of the grand total — get answers that match listed wrong-answer choices.
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 7 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. Of 35 boys and 58 girls who said yes, and 42 boys and 70 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 7/41
- B 93/205
- C 58/205
- D 58/93
Worked solution
Answer: C — 58/205
Total students = 35 + 58 + 42 + 70 = 205. Girls who said yes = 58. Probability = 58/205 = 58/205.
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A school surveyed students about a proposed schedule change. Of 51 boys and 78 girls who said yes, and 24 boys and 39 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 43/64
- B 17/64
- C 13/32
- D 26/43
Worked solution
Answer: C — 13/32
Total students = 51 + 78 + 24 + 39 = 192. Girls who said yes = 78. Probability = 78/192 = 13/32.
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A school surveyed students about a proposed schedule change. Of 22 boys and 69 girls who said yes, and 69 boys and 62 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 91/222
- B 23/74
- C 69/91
- D 11/111
Worked solution
Answer: B — 23/74
Total students = 22 + 69 + 69 + 62 = 222. Girls who said yes = 69. Probability = 69/222 = 23/74.
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A school surveyed students about a proposed schedule change. Of 79 boys and 28 girls who said yes, and 41 boys and 65 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 79/213
- B 28/107
- C 28/213
- D 107/213
Worked solution
Answer: C — 28/213
Total students = 79 + 28 + 41 + 65 = 213. Girls who said yes = 28. Probability = 28/213 = 28/213.
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A school surveyed students about a proposed schedule change. Of 79 boys and 53 girls who said yes, and 26 boys and 64 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 79/222
- B 22/37
- C 53/222
- D 53/132
Worked solution
Answer: C — 53/222
Total students = 79 + 53 + 26 + 64 = 222. Girls who said yes = 53. Probability = 53/222 = 53/222.
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A school surveyed students about a proposed schedule change. Of 55 boys and 30 girls who said yes, and 62 boys and 63 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 1/7
- B 17/42
- C 11/42
- D 6/17
Worked solution
Answer: A — 1/7
Total students = 55 + 30 + 62 + 63 = 210. Girls who said yes = 30. Probability = 30/210 = 1/7.
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A school surveyed students about a proposed schedule change. Of 23 boys and 31 girls who said yes, and 25 boys and 53 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 31/54
- B 23/132
- C 31/132
- D 9/22
Worked solution
Answer: C — 31/132
Total students = 23 + 31 + 25 + 53 = 132. Girls who said yes = 31. Probability = 31/132 = 31/132.
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.