{"blocks": [{"key": "5d4ae16d", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "928c73c1", "text": "Radioactive-decay style process: 100 independent particles, each has a known half-life. Interviewer wants theoretical probability of how many survive after a given time.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "634e9659", "text": "Question", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "0bb90e67", "text": "Given 100 identical particles with half-life H (each decays independently with exponential distribution), derive the probability that exactly k (or at least one) particles remain undecayed after time t.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "f81c98fa", "text": "Hints", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "041c49ef", "text": "Recall exponential survival function P(T>t)=e^{-λt} where λ=ln2/H; use Binomial distribution on independent survival events.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}], "entityMap": {}}