14 QUESTIONS · NO TIMER

Probability Surprises

Count the outcomes and notice when new information changes the sample space.

Find the useful constraint

Probability often becomes clearer when you list equally likely outcomes. Two independent fair coins give HH, HT, TH, and TT. Exactly one head means two outcomes; at least one head means three. After conditioning on at least one head, TT is excluded and the remaining outcomes must be compared within that smaller set. Be careful: a reporting or selection process can change which outcomes are equally likely.

Slow down at the decision

Before choosing, restate what the question actually requires. Separate a condition that must hold from a detail that merely sounds familiar. Try each choice against the complete rule, rather than stopping at the first plausible answer. A counterexample can eliminate a confident guess faster than a long calculation. These rounds have no countdown: reading the explanation is part of the experience, not a penalty for a mistake.

A fair challenge

Each question provides its assumptions and has one intended answer. Pattern questions state their rules instead of asking you to guess an author's private pattern. Probability questions specify what is random and what information is known. Use the explanation to identify the exact step that changed your answer. Then try a fresh round; recognizing a principle in a different situation matters more than memorizing an answer letter.

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Can you figure these out?

Five puzzles. No timer. An explanation after every answer.

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