請問這題Probability點計及點解?
2011-10-24 3:56 am
It is known that the number of bacteria of a certain kind per cm3 of sea water follows a Poisson distribution wit mean 3. Independent samples of 1 cm3 of sea water are taken form various bays and are inspected.(a) Find the probability that the sample contains 3 or more bacteria.(b) If 5 samples are taken, find the probability that 2 of them contain 3 or more bacteria.
回答 (1)
2011-10-24 4:07 pm
✔ 最佳答案
(a) P(Contains 3 or more bacteria) = 1 - P(No bacteria) - P(Contains 1 bacteria) - P(Contain 2 bacteria) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]= 1 - e^(-3)[1 + 3 + 9/2] = 1 - e^(-3)(8.5) = 0.5768
(b) This is a binomial dist. with n = 5 and p = 0.5768
P(2 out of 5 samples containing 3 or more bacteria) = (5C2)(0.5768^2)(1 - 0.5768)^3 = 0.25217.
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