SOLUTION: Assume that the OUHK mail-order box employs three clerks, A, B and C, who pull items from shelves and assemble them for subsequent verification and packaging. Clerk A makes a mista

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Question 1159631: Assume that the OUHK mail-order box employs three clerks, A, B and C, who pull items from shelves and assemble them for subsequent verification and packaging. Clerk A makes a mistake in 1% of his order (gets a wrong item or the wrong quantity), clerk B makes 5% mistakes, and clerk C makes 3% mistakes. If the person A, B and C fill 30%, 40% and 30% of all orders respectively, what are the probabilities that:
(a) a mistake will be made in an order.
(b) if a mistake is made in an order, the order was filled by the clerk A.
(c) if an order is not filled by the clerk A, a mistake is made in that order

Found 2 solutions by Boreal, jim_thompson5910:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
=====ok=======wrong====total
A-----297----------3---------300
B-----380---------20---------400
C-----291----------9---------300
Tot---968---------32--------1000
a. 3.2% probability of a mistake
b. 3/32 or 9.375% it is due to A.
c. B and C have 29 mistakes in 671 orders or 4.32%

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

The tutor @Boreal has a great table set up showing an example of 1000 orders total, and how those orders are distributed among the three workers (also whether a certain order is a mistake or not).

However, their answer for part C is not correct. The answer for part C should be 29/700 = 0.04142857142858 approximately since there are 20+9 = 29 wrong orders made by clerk B or clerk C, out of 400+300 = 700 orders total by those two clerks. Basically you ignore row A entirely as we know for certain that the order was not filled by clerk A.

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