[問題] 一題簡單機率問題
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小妹最近在準備考試
最近準備到一題,我寫的答案跟解答不一樣,可是我想來想去也不知道我的問題在哪裡,
因此跪求賜教orz
題目:
A store has 80 modems in its inventory, 30 coming from Source A and remainder
from Source B. Of the modems from Source A,20% are defective. Of the modems
from Source B,8% are defective.
Calculate the probability that exactly two out of the random sample of five
modems from the store's inventory are defective
(a)0.010 (b)0.078 (c)0.102 (d)0.105 (e)0.125
解答是(c)
算法是先將80個產品中所有defective的產品先算出來
30*0.2+50*0.08=10(個)
所以有80-10=70(個)產品是合格的
題目所求是隨機挑選5個中兩個要不合格,
所以
10 70
( ) *( )
__2_____3___=0.102466 所以選(c)
80
( )
5
我的算法是
因為我認為0.2=P(defective|from SourceA)
0.08=P(defective|from SourceB)
5個中選2個的機率直觀會選擇二項是分配吧(我想...)
再者
P(from Source A)=30/80=3/8
P(from Source B)=50/80=5/8
P(defective)=(3/8)P(defective|from Source A)+(5/8)P(defective|from Source B)
=(3/8)(0.2)+(5/8)(0.08)=0.128=1/8
所以我很直觀的就寫
5
( )(1/8)^2 *(7/8)^3=0.1046
2
所以我選(D)
我想請問各位高手,我的問題在哪裡呢?謝謝大家!!
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