Question 729645
.
Three machines A, B and C produce respectively 60%, 30% and 10 % of the total number of items of a factory. 
The percentage of defectives output of these machines are 2%, 3% and 4%, respectively. 
If an item is selected at random and is found defective. 
Find the probability that the selected item was produced by machine C.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The probability that this selected item was produced by the machine C is the ratio

          percentage of defective items produced by machine C
    P = --------------------------------------------------------------- = {{{(0.1*0.04)/(0.6*0.02 + 0.3*0.03 + 0.1*0.04)}}} = 0.16.
          percentage of defective items produced by all three machines


<U>ANSWER</U>.  The probability that the selected item was produced by machine C is 0.16, or 16%.
</pre>

Solved.