Probability Brain-Teasers

Problem Standard probability brain-teasers — dice, coins, and conditional-probability scenarios — asking the candidate to reason through the setup out loud.

Be ready to discuss

• Expected-value problems: the expected number of coin flips to see two heads in a row, solved by setting up states and recurrence relations rather than simulating.
• Conditional probability: Monty Hall and its variants, the Bayes'-theorem framing, and why the intuitive answer is wrong — plus classic base-rate/false-positive medical-test problems.
• Card and ordering problems: the probability one specific card appears before another in a shuffled deck, and why symmetry arguments collapse a messy calculation to 1/2.
• Core technique: define the sample space precisely, decide whether events are independent, and choose between counting, conditioning, symmetry, or linearity of expectation — naming the tool before computing.
• Linearity of expectation as the workhorse: it holds even when events are dependent, which cracks problems that look intractable (expected number of matches, coupon collector).
• What's evaluated: structured reasoning under ambiguity — stating assumptions, showing the setup, and handling follow-up variations posed on the fly matters more than the exact final number.
• Practical delivery: sanity-check the answer against an extreme case, and say when a simulation would settle it faster than a closed form.