{"blocks": [{"key": "aeef5ce4", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "82df534f", "text": "For n users independently asked to link a Coinbase wallet, each links with probability p.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "ecb23a91", "text": "Question", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "f9e8a69b", "text": "What is the expected number of users who link their wallet? What is the probability that at least one user links a wallet? Given that at least one of users A or B links a wallet, what is the probability that both A and B link?", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "ab2671d2", "text": "Hints", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "9537e3ab", "text": "Use linearity of expectation and independence: E[X]=np; P(at least one)=1−(1−p)^n; apply conditional probability for the final part.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}], "entityMap": {}}