{"blocks": [{"key": "af0c153a", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "d2491530", "text": "Online assessment requires candidates to solve non-formulaic probability puzzles within strict proctoring constraints.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "97f59068", "text": "Question", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "0e561151", "text": "Let X1,…,Xn be i.i.d. Bernoulli(p). Derive a closed-form expression for P(Σ_i X_i is even). A fair coin is flipped until two consecutive identical outcomes appear. What is the expected number of flips?", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "7455b2c1", "text": "Hints", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "2390f531", "text": "Use moment-generating tricks or parity arguments for the first; write a recurrence or Markov chain for the second.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}], "entityMap": {}}