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

Score band 500-600 · Problem Solving & Data Analysis

Probability and Two-Way Tables drills for 500-600

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Targeted practice for students currently scoring in the 500-600 range, drilling exclusively on probability and two-way tables.

What a 500-600 scorer needs from this topic

The 500 to 600 score band is where most students start when they first sit a practice SAT. Questions in this band still test single concepts, but the numbers get less friendly and the stems get longer. The College Board starts adding distractors that punish students who solved correctly but answered the wrong question. To break out of this band, you need to combine accuracy on the easy questions with a willingness to slow down on the medium ones. Building-band drills focus on the most common medium-difficulty patterns released by the College Board: word-problem translation, multi-step arithmetic, two-variable systems with messy coefficients, and proportional reasoning with awkward unit conversions.

For Probability and Two-Way Tables specifically, students in the 500-600 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 500-600 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. 500-600 easy Conditional Probability

    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?

    1. A 74/131
    2. B 131/211
    3. C 74/211
    4. 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.

  2. 500-600 easy Compound and Independent Events

    A school surveyed students about a proposed schedule change. 72 boys and 23 girls said yes; 70 boys and 80 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?

    1. A 72/245
    2. B 72/95
    3. C 23/95
    4. D 19/49
    Worked solution

    Answer: B — 72/95

    Conditional probability uses only the subset that said yes as the denominator. That subset is 72 + 23 = 95. Boys in that subset = 72. Probability = 72/95 = 72/95.

  3. 500-600 medium Simple Probability

    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?

    1. A 91/222
    2. B 23/74
    3. C 69/91
    4. 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.

  4. 500-600 medium Probability from Two-Way Tables

    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?

    1. A 38/79
    2. B 41/167
    3. C 79/167
    4. 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.

  5. 500-600 medium Conditional Probability

    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?

    1. A 60/83
    2. B 60/221
    3. C 23/221
    4. 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.

  6. 500-600 medium Compound and Independent Events

    A school surveyed students about a proposed schedule change. 53 boys and 79 girls said yes; 20 boys and 20 girls said no. Given that a randomly chosen student said yes, what is the probability the student is a boy?

    1. A 33/43
    2. B 53/172
    3. C 53/132
    4. D 79/132
    Worked solution

    Answer: C — 53/132

    Conditional probability uses only the subset that said yes as the denominator. That subset is 53 + 79 = 132. Boys in that subset = 53. Probability = 53/132 = 53/132.

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.

Other 500-600 drills