本區搜索:
Yahoo!字典
打印

[M2] help!!!!CAN'T SOLVE THE QUESTION

help!!!!CAN'T SOLVE THE QUESTION

In a manufacturing process, each item leaving an assembly line will be examined by two inspectors: A and B individually. Based on past experiences, Inspector A detects 60% of the defective items. If the defective items are not detected by Inspector A, 90% of them will be detected by Inspector B. However, 60% of the defective items are not detected by Inspector B given that they are detected by Inspector A.
(a)Draw a probability tree
(b)What is the probability that a defective item is detected by at least one of the inspectors?
(c)What is the probability that a defective item is detected by Inspector A, given that it is detected by Inspector B?


em35 i can't solve this questions for an hour
please someone help me!!!!
   

TOP

[隱藏]
Let  A be the event that the defective item is detected by Inspector A.
Let  B be the event that the defective item is detected by Inspector B.
Provided by the question, we have
P(A)=0.6, P(B|A')=0.9 and P(B'|A)=0.6.

(a) The probability tree is shown as follows:
             0.4
0.6.     ---------B
-------A   0.6
            ---------B'
             0.9
0.4.     ---------B
-------A'  0.1
             --------B'

(b) P(A or B) = 1 - P(A' and B')  =  1-(0.4)(0.1)= 1-0.04=0.96
(c) By Bayes' Thm., P(A|B) = (0.6)(0.4)/( (0.6)(0.4)+(0.4)(0.9) ) = 0.24/(0.24+0.36) = 0.24/0.6 = 0.4

TOP

重要聲明:小卒資訊論壇 是一個公開的學術交流及分享平台。 論壇內所有檔案及內容 都只可作學術交流之用,絕不能用商業用途。 所有會員均須對自己所發表的言論而引起的法律責任負責(包括上傳檔案或連結), 本壇並不擔保該等資料之準確性及可靠性,且概不會就因有關資料之任何不確或遺漏而引致之任何損失或 損害承擔任何責任(不論是否與侵權行為、訂立契約或其他方面有關 ) 。