Quandaries and Queries


A certain drug is found to be effective 80% of the time. Find the probability of successful treatment in two out of four cases.





This is a binomial experiment. The assumptions are that you have a simple experiment (treat one individuat with the drug), that you repeat many times (n times), and the repetitions are independet (the probability that the treatment is effective on any particular individual is independent of the results for previous individuals). If the probability that the drug is effective is p, then the probability that the drug is effective on exactly k of the n people who received the drug is

C(n,k) pk (1 - p)n - k In your example n = 4, k = 2, and p = 0.8 so the probability is C(4,2) 0.82 (1 - 0.8)4 - 2 = 0.1536


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