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標題:

一條數學 急用15分

發問:

in a recent finding in a city of australia , the probability of giving birth to a boy is 45% (a) a family prepares to have 2 children. find the probabilities that all of them are boys. (b) the other family prepares to have 2 children. find the probabilities that at least one of them is a boy.

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最佳解答:

It is given in the question that P(boy) = 0.45 Assume that the gender of each child is independent of others. (a) P(2 boys) = P(boy and boy) = P(boy) × P(boy) = 0.45 × 0.45 = 0.2025 (b) P(at least 1 boy) = 1 - P(no boy) = 1 - P(not boy and not boy) = 1 - P(not boy) × P(not boy) = 1 - (1 - 0.45) × (1 - 0.45) = 1 - (1 - 0.45)2 = 1 - 0.552 = 1 - 0.3025 = 0.6975 2015-04-12 15:36:20 補充： (b) Alternative method: Possibilties are (1) Boy, Girl (2) Girl, Boy (3) Boy, Boy Probability = 0.45 × 0.55 + 0.55 × 0.45 + 0.45 × 0.45 = 2(0.45)(0.55) + 0.452 = 0.495 + 0.2025 = 0.6975 2015-04-12 18:23:29 補充： 若 (a) 題目修正為 A family prepares to have 3 children. find the probabilities that all of them are boys. 那麼答案就是： (0.45)3 = 0.091125 2015-04-12 18:23:39 補充： 若 (a) 題目修正為 A family prepares to have 3 children. find the probabilities that all of them are boys. 那麼答案就是： (0.45)3 = 0.091125

其他解答:

(a)個條係3 children打少左一個
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