{"blocks": [{"key": "f1def726", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "452d8a39", "text": "Users are prompted to link their Coinbase wallet; each user independently links with probability p.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "53970028", "text": "Question", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "e0af13f6", "text": "Given n independent users with link probability p: 1) What is the expected number who link? 2) What is the probability at least one user links? 3) For two users A and B, what is the probability both link conditioned on at least one of them linking?", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "0944e42f", "text": "Hints", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "88f075bf", "text": "Use linearity of expectation; at-least-one equals 1−(1−p)^n; conditional P(A∩B | A∪B) = p^2 /(2p−p^2).", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}], "entityMap": {}}