cc asked in 科學數學 · 1 decade ago

機率統計~~~問一題機率題!!

Suppose there are 3 defective items in a lot of 50 items.A sample of size 10 is taken at random and without replacement.Let X denoted the number of defective items in the sample.Find probability that the sample contains

(a) Exactly 1 defective item.

(b) At most 1 defective item.

如果可以請幫忙附上此題的中文意思~~~感激不盡^^

1 Answer

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  • 1 decade ago
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    Suppose there are 3 defective items in a lot of 50 items.

    假設在50個物品中有3個瑕玼品。

    A sample of size 10 is taken at random and without replacement.

    隨機從50個物品中取出10個,取出後不放回。

    Let X denoted the number of defective items in the sample.

    令X表示這10個物品中的瑕玼品數目。

    Find probability that the sample contains

    求以下情形的機率

    (a) Exactly 1 defective item.恰含1個瑕玼品。

    [解]

    所求 = n(1個瑕玼品,9個良品)/全部情形

    = [C(3,1)*C(47,9)]/C(50,10)

    = 39/98

    = 0.397959...

    (b) At most 1 defective item.至多有一個瑕玼品。

    用反面解法:

    所求 = P( 沒瑕玼品) + P(恰1個瑕玼品)

    = [n(10個良品)/全部情形] + 39/98

    = [C(47,10)]/C(50,10) +39/98

    = 221/245

    = 0.902040...

    2006-10-26 02:21:25 補充:

    上面打錯了(b) 是正面解法反面解法是求 1 - P( 恰2個瑕玼品) - P(恰3個瑕玼品)

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