ScoreReady SAT
Drill by score band: 400–500 500–600 600–700 700–800

Score band 600-700 · Problem Solving & Data Analysis

Probability and Two-Way Tables drills for 600-700

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Targeted practice for students currently scoring in the 600-700 range, drilling exclusively on probability and two-way tables.

What a 600-700 scorer needs from this topic

The 600 to 700 band is the largest plateau on the SAT Math section. Students stuck here are usually accurate on every easy question and most medium questions, but they lose four to six points to harder algebra and to one or two arithmetic slips per section. Breaking out of this band requires both a deeper toolbox and a faster execution speed on the questions you already know how to do. Strengthening-band drills target the harder question patterns: quadratic systems, exponential and rational manipulation, function composition, conditional probability, and the geometry questions that require an extra construction line you must add to the figure yourself.

For Probability and Two-Way Tables specifically, students in the 600-700 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 600-700 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. 600-700 medium Simple Probability

    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?

    1. A 79/213
    2. B 28/107
    3. C 28/213
    4. 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.

  2. 600-700 medium Probability from Two-Way Tables

    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?

    1. A 35/124
    2. B 2/9
    3. C 7/9
    4. 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.

  3. 600-700 medium Conditional Probability

    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?

    1. A 72/187
    2. B 109/187
    3. C 72/109
    4. 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.

  4. 600-700 medium Compound and Independent Events

    A school surveyed students about a proposed schedule change. 80 boys and 38 girls said yes; 37 boys and 50 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?

    1. A 40/59
    2. B 118/205
    3. C 16/41
    4. D 19/59
    Worked solution

    Answer: A — 40/59

    Conditional probability uses only the subset that said yes as the denominator. That subset is 80 + 38 = 118. Boys in that subset = 80. Probability = 80/118 = 40/59.

  5. 600-700 medium Simple Probability

    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?

    1. A 79/222
    2. B 22/37
    3. C 53/222
    4. 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.

  6. 600-700 medium Probability from Two-Way Tables

    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?

    1. A 74/241
    2. B 134/241
    3. C 37/67
    4. 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.

  7. 600-700 hard Conditional Probability

    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?

    1. A 12/17
    2. B 68/131
    3. C 20/131
    4. 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.

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.

Other 600-700 drills