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Kidorizon · Grades 9–12 · free printable · kidorizon.com

Spot the Mistake: Logic & Probability

Name: ______________________Date: ______________

Each box has four statements written to look like an AI answer. Exactly one is wrong. Circle its letter and justify your choice in a sentence.

  1. 1. Chance

    A kid asks the AI: “Explain some probability basics.”

    The AI answers: Here are four probability facts:

    • Statement A: Flipping a fair coin twice, the chance of two heads is 1/4.
    • Statement B: The chance of rolling a 6 on a fair die is 1/6.
    • Statement C: After five heads in a row, a fair coin is now more likely to land tails.
    • Statement D: With two fair dice, the chance of a sum of 7 is 1/6.

    Which statement is wrong? Circle its letter, then tell someone how you decided.

  2. 2. Probability rules

    A kid asks the AI: “What are the rules of probability?”

    The AI answers: Here are four rules:

    • Statement A: For independent events, P(A and B) = P(A) × P(B). With 0.3 and 0.5 that is 0.15.
    • Statement B: The probabilities of all outcomes in a sample space add up to 1.
    • Statement C: A probability can be 1.4 if an event is very likely.
    • Statement D: P(not A) = 1 − P(A).

    Which statement is wrong? Circle its letter, then tell someone how you decided.

  3. 3. If-then logic

    A kid asks the AI: “Explain converse and contrapositive.”

    The AI answers: Take the rule "If it rains, the ground is wet." Here are four statements:

    • Statement A: The contrapositive is: if the ground is not wet, then it did not rain.
    • Statement B: The converse is: if the ground is wet, then it rained, and it must be true whenever the original is true.
    • Statement C: An argument is sound if it is valid and all its premises are true.
    • Statement D: A valid argument with a false premise can still have a true conclusion.

    Which statement is wrong? Circle its letter, then tell someone how you decided.

  4. 4. Algebra and logs

    A kid asks the AI: “Check my algebra facts.”

    The AI answers: Here are four algebra facts:

    • Statement A: The slope of y = 3x − 2 is 3.
    • Statement B: x² − 9 = (x − 3)(x + 3).
    • Statement C: The solutions of x² = 16 are 4 and −4.
    • Statement D: log₂ 8 = 4.

    Which statement is wrong? Circle its letter, then tell someone how you decided.

  5. 5. Data and sampling

    A kid asks the AI: “How do I read a survey fairly?”

    The AI answers: Here are four statistics facts:

    • Statement A: Larger random samples generally give more reliable estimates.
    • Statement B: Correlation does not prove causation.
    • Statement C: An open online poll that anyone chooses to answer is a random sample of everyone.
    • Statement D: One extreme outlier can pull the mean more than the median.

    Which statement is wrong? Circle its letter, then tell someone how you decided.

  6. 6. Counting arrangements

    A kid asks the AI: “Explain permutations and combinations.”

    The AI answers: Here are four counting facts:

    • Statement A: 3 different books can be arranged on a shelf in 6 ways.
    • Statement B: Choosing 2 of 5 people for a pair can be done in 10 ways.
    • Statement C: 4 people can stand in a line in 24 ways.
    • Statement D: Choosing 3 of 6 people for a team can be done in 120 ways.

    Which statement is wrong? Circle its letter, then tell someone how you decided.

Kidorizon practice sheets build thinking skills. They are not a test or assessment. More free activities at kidorizon.com/play