Math · Problem-Solving and Data Analysis

    Probability and Conditional Probability

    Compute probabilities from two-way tables and basic experiments.

    What the SAT Tests

    Digital SAT probability questions usually involve reading a two-way table and computing a conditional probability. The challenge is understanding which row or column total to divide by.

    Key Tips for Probability and Conditional Probability

    • Probability = favorable outcomes / total outcomes.
    • Conditional probability restricts the sample space to the given row or column.
    • Independent events multiply; mutually exclusive events add.

    How to recognize Probability and Conditional Probability questions

    • Look for Problem-Solving and Data Analysis signals: equations, graphs, tables, variables, units, or words that describe a relationship.
    • Before solving, decide whether the answer should be a value, expression, coordinate, graph feature, or interpretation.
    • The official College Board skill label is Probability and conditional probability; match your practice misses to that label when reviewing.

    Fast solving workflow

    1. Translate the givens into an equation, graph, table, or labeled diagram before using answer choices.
    2. Choose the fastest method: mental math for one-step work, paper algebra for clean symbolic steps, Desmos for intersections/tables/roots, and substitution for ordered answer choices.
    3. Check the final answer against the question stem, especially units, signs, and whether it asks for x, y, a sum, a coefficient, or an interpretation.

    Common traps

    • Using the wrong denominator in a percent, rate, or probability question.
    • Confusing correlation with causation in data claims.
    • Extrapolating outside the data range when the question does not justify it.

    Sample Probability and Conditional Probability Questions

    These are real practice questions pulled from our Digital SAT bank. Try each one before reading the highlighted correct answer.

    1. Question 1 · Easy
      At a conference hall, there are 625 attendees in total. Each attendee is in exactly one of room A, room B, or room C. If one attendee is chosen at random, the probability of choosing an attendee in room A is 0.64, and the probability of choosing an attendee in room B is 0.28. How many attendees are in room C?
      • A. 8
      • B. 50Correct
      • C. 112
      • D. 225
    2. Question 2 · Easy
      A sleep study consisted of 52 participants, of which 47 participants each had an average of more than 110 minutes of rapid eye movement (REM) sleep per night. If a participant from this sleep study is selected at random, what is the probability of selecting a participant that had an average of more than 110 minutes of REM sleep per night?
      • A.
      • B.
      • C. Correct
      • D.
    3. Question 3 · Easy
      At a museum, there are a total of 500 visitors. Each visitor is located in either room A, room B, or room C. If one of these visitors is selected at random, the probability of selecting a visitor who is located in room A is , and the probability of selecting a visitor who is located in room B is . How many visitors are located in room C?
      • A.
      • B. Correct
      • C.
      • D.

    Practice Probability and Conditional Probability Questions

    Drill probability and conditional probability questions in the Digital SAT Math question bank, or take a full-length practice module to see how this skill appears under test conditions.

    Practice blockWhat to doMove on when
    WarmupSolve 10 untimed probability and conditional probability questions and write the rule used for each.You can explain 8 of 10 without reading the explanation.
    Timed drillSolve 20 filtered bank questions at real module pace.Accuracy is at least 80% and misses are not repeating.
    TransferTake a mixed timed module and mark each Problem-Solving and Data Analysis miss.The skill still holds up when mixed with other question types.

    FAQs

    What is Probability and Conditional Probability on the Digital SAT?

    Digital SAT probability questions usually involve reading a two-way table and computing a conditional probability. The challenge is understanding which row or column total to divide by.

    How hard are probability and conditional probability questions?

    Probability and Conditional Probability questions appear at every difficulty level on the Digital SAT Math section. The hardest versions gate access to the top scaled scores in the hard Module 2.

    How do I practice probability and conditional probability?

    Use the 1600.now question bank to filter for probability and conditional probability questions, solve at least 20 in a row, and review every miss with the written explanation.

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