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Probability ( Fundamental )
發問:
假設現在有27個藍色波，37個黃色波，36個紅色波，n=100。現在random地抽 5個波 at a time with replacement. 咁我想問 Probability of at most 2 blue balls 同埋 Probability of at most 2 blue balls give than at least two balls are not blue. 點計 thank you >
最佳解答:
假設現在有27個藍色波，37個黃色波，36個紅色波，n=100。現在random地抽 5個波 at a time with replacement. = = = = = (1) B = blue ball N = not blue ball 由於有 replacement，每次都係由 100 balls 抽出 1 ball。每一次： P(B) = 27/100 P(N) = 1 - (27/100) = 73/100 P(at most 2 B) = P(0B5N) + P(1B4N) + P(2B3N) = (73/100)^5 + 5C1*(27/100)*(73/100)^4 + 5C2*(27/100)^2*(73/100)^3 = 4371384029/5000000000 or 0.8742768058 = = = = = (2) P([at most 2B] and [at least 2N]) = P([at most 2B] and [at most 3B]) = P(at most 2B) = 0.8742768058 P(at least 2N) = P(0B5N) + P(1B4N) + P(2B3N) + P(3B2N) = 0.8742768058 + 5C3*(27/100)^3*(73/100)^2 = 0.9791675128 P(at most 2B | at least 2N) = P([at most 2B] and [at least 2N]) / P(at least 2N) = 0.8742768058/0.9791675128 = 820301/918716 or 0.8928776684
其他解答:
to樓上: 一次抽5個|||||係一次抽 5 個定係每次抽 1 個兼每次 replacement?
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