# 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

- terry wangLv 41 decade agoFavorite Answer
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)