Probability and Two-Way Tables · Sub-skill drill
Conditional Probability
Conditional probability is the probability of event A given that event B has occurred, written P(A|B). The formula is P(A and B) divided by P(B). On the SAT this is almost always computed from a two-way table by reading the count in the (A and B) cell and dividing by the row or column total for B. Identifying B correctly is the entire skill. Underline the conditioning phrase ('among those who...', 'given that...') in the prompt before computing.
How this sub-skill is tested on the SAT
Conditional probability is the probability of event A given that event B has occurred, written P(A|B). The formula is P(A and B) divided by P(B). On the SAT this is almost always computed from a two-way table by reading the count in the (A and B) cell and dividing by the row or column total for B. Identifying B correctly is the entire skill. Underline the conditioning phrase ('among those who...', 'given that...') in the prompt before computing.
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. Of 76 boys and 80 girls who said yes, and 59 boys and 36 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 80/251
- B 156/251
- C 20/39
- D 76/251
Worked solution
Answer: A — 80/251
Total students = 76 + 80 + 59 + 36 = 251. Girls who said yes = 80. Probability = 80/251 = 80/251.
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A school surveyed students about a proposed schedule change. Of 57 boys and 74 girls who said yes, and 29 boys and 51 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 74/131
- B 131/211
- C 74/211
- D 57/211
Worked solution
Answer: C — 74/211
Total students = 57 + 74 + 29 + 51 = 211. Girls who said yes = 74. Probability = 74/211 = 74/211.
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A school surveyed students about a proposed schedule change. Of 23 boys and 60 girls who said yes, and 62 boys and 76 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 60/83
- B 60/221
- C 23/221
- D 83/221
Worked solution
Answer: B — 60/221
Total students = 23 + 60 + 62 + 76 = 221. Girls who said yes = 60. Probability = 60/221 = 60/221.
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A school surveyed students about a proposed schedule change. Of 37 boys and 72 girls who said yes, and 47 boys and 31 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 72/187
- B 109/187
- C 72/109
- D 37/187
Worked solution
Answer: A — 72/187
Total students = 37 + 72 + 47 + 31 = 187. Girls who said yes = 72. Probability = 72/187 = 72/187.
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A school surveyed students about a proposed schedule change. Of 20 boys and 48 girls who said yes, and 26 boys and 37 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 12/17
- B 68/131
- C 20/131
- D 48/131
Worked solution
Answer: D — 48/131
Total students = 20 + 48 + 26 + 37 = 131. Girls who said yes = 48. Probability = 48/131 = 48/131.
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A school surveyed students about a proposed schedule change. Of 31 boys and 28 girls who said yes, and 29 boys and 49 girls who said no, a student is selected at random. What is the probability the student is a girl who said yes?
- A 31/137
- B 28/59
- C 59/137
- D 28/137
Worked solution
Answer: D — 28/137
Total students = 31 + 28 + 29 + 49 = 137. Girls who said yes = 28. Probability = 28/137 = 28/137.
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.