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標題:
(20pt) 有關Advance的Probability問題
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A distributor sells rubber bands in packages of 100 and guarantees that at most 10% are defective. A consumer controls each package by randomly drawing 10 bands without replacement.If the sample contains no defective rubber bands, he accepts the package.Otherwise, he rejects it.(a) Find the probability that in... 顯示更多 A distributor sells rubber bands in packages of 100 and guarantees that at most 10% are defective. A consumer controls each package by randomly drawing 10 bands without replacement. If the sample contains no defective rubber bands, he accepts the package. Otherwise, he rejects it. (a) Find the probability that in this process the consumer rejects a package which contains 10 defectives. (b) Find the probability that any given package is accepted although it contains 20 defectives
(a) There are 10 defectives in 100 rubber bands. Randomly choose 1 rubber band, Pr(defective) = 10/100 = 0.1 and Pr(not defective) = 1 - 0.1 = 0.9 Pr(reject the package) = Pr(at least one is defective out of 10 rubber bands) = 1 - Pr(all 10 rubber bands are not defective) = 1 - 0.91? = 0.6513215599 ==== (b) There are 20 defectives in 100 rubber bands. Randomly choose 1 rubber band, Pr(defective) = 20/100 = 0.2 and Pr(not defective) = 1 - 0.2 = 0.8 Pr(accept the package) = Pr(all 10 rubber bands are not defective) = 0.81? = 0.1073741824
其他解答:
(20pt) 有關Advance的Probability問題
發問:
A distributor sells rubber bands in packages of 100 and guarantees that at most 10% are defective. A consumer controls each package by randomly drawing 10 bands without replacement.If the sample contains no defective rubber bands, he accepts the package.Otherwise, he rejects it.(a) Find the probability that in... 顯示更多 A distributor sells rubber bands in packages of 100 and guarantees that at most 10% are defective. A consumer controls each package by randomly drawing 10 bands without replacement. If the sample contains no defective rubber bands, he accepts the package. Otherwise, he rejects it. (a) Find the probability that in this process the consumer rejects a package which contains 10 defectives. (b) Find the probability that any given package is accepted although it contains 20 defectives
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最佳解答:(a) There are 10 defectives in 100 rubber bands. Randomly choose 1 rubber band, Pr(defective) = 10/100 = 0.1 and Pr(not defective) = 1 - 0.1 = 0.9 Pr(reject the package) = Pr(at least one is defective out of 10 rubber bands) = 1 - Pr(all 10 rubber bands are not defective) = 1 - 0.91? = 0.6513215599 ==== (b) There are 20 defectives in 100 rubber bands. Randomly choose 1 rubber band, Pr(defective) = 20/100 = 0.2 and Pr(not defective) = 1 - 0.2 = 0.8 Pr(accept the package) = Pr(all 10 rubber bands are not defective) = 0.81? = 0.1073741824
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