ScoreReady SAT
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Score band 700-800 · Problem Solving & Data Analysis

Probability and Two-Way Tables drills for 700-800

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Targeted practice for students currently scoring in the 700-800 range, drilling exclusively on probability and two-way tables.

What a 700-800 scorer needs from this topic

The 700 to 800 band is the elite tier of SAT Math. Reaching it requires zero careless errors and confident solves on the hardest one or two questions in each module. Mastery-band drills focus on the hardest released questions: multi-concept problems that combine two or three skills in one stem, abstract algebraic manipulation with parameters instead of numbers, geometry questions that require a clever construction, and data-analysis questions that test conceptual understanding rather than computation. At this level, speed matters as much as accuracy, because the only way to leave time for the hardest questions is to dispatch the easy and medium ones in well under a minute each.

For Probability and Two-Way Tables specifically, students in the 700-800 band need to focus on the question patterns the College Board uses at this difficulty level. Compute probabilities from tables and basic counting. The questions below are pulled from the ScoreReady question bank and filtered to the 700-800 band based on difficulty calibration that matches publicly released College Board practice materials.

Drill these untimed first. Once you can produce a clean worked solution on paper for every question without notes, switch to timed mode and aim for under 75 seconds per question. That pace is roughly the average time per question on the actual SAT Math section, and it leaves time for the harder questions you will see at the end of each module.

Practice set

  1. 700-800 hard Compound and Independent Events

    A school surveyed students about a proposed schedule change. 36 boys and 80 girls said yes; 68 boys and 35 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?

    1. A 20/29
    2. B 12/73
    3. C 116/219
    4. D 9/29
    Worked solution

    Answer: D — 9/29

    Conditional probability uses only the subset that said yes as the denominator. That subset is 36 + 80 = 116. Boys in that subset = 36. Probability = 36/116 = 9/29.

  2. 700-800 hard Simple Probability

    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?

    1. A 1/7
    2. B 17/42
    3. C 11/42
    4. 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.

  3. 700-800 hard Probability from Two-Way Tables

    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?

    1. A 42/97
    2. B 97/169
    3. C 55/97
    4. 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.

  4. 700-800 hard Conditional Probability

    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?

    1. A 31/137
    2. B 28/59
    3. C 59/137
    4. 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.

  5. 700-800 hard Compound and Independent Events

    A school surveyed students about a proposed schedule change. 30 boys and 47 girls said yes; 66 boys and 45 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?

    1. A 47/77
    2. B 15/94
    3. C 30/77
    4. D 77/188
    Worked solution

    Answer: C — 30/77

    Conditional probability uses only the subset that said yes as the denominator. That subset is 30 + 47 = 77. Boys in that subset = 30. Probability = 30/77 = 30/77.

  6. 700-800 hard Simple Probability

    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?

    1. A 31/54
    2. B 23/132
    3. C 31/132
    4. 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.

How to use these drills to climb a band

Climbing from one score band to the next requires a different study mix than climbing within a band. Within a band, you are mostly fixing careless errors and pattern-recognizing the question types you already understand. Climbing to the next band means adding new question types to your toolbox — patterns you currently recognize but cannot solve fluently. The 700–800 set in this drill is exactly that toolbox for students currently in the 600–700 range.

The single most reliable indicator that you are ready to move up a band is being able to explain a worked solution to someone else, in your own words, without referring to notes. Practice this with one classmate or one parent per week. The act of teaching exposes the gaps your timed solves did not.

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