Question 1205005
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Let's say 1000 items are produced. There's nothing particularly special about this value other than its some large round number. Feel free to pick something else if you want.


15% of those 1000 items are defective, so we have 0.15*1000 = 150 defective items and 1000-150 = 850 working items.


The inspector gets things wrong 10% of the time.
Of the 150 defective items, 10% of them are considered "good" when they shouldn't be. That's 0.10*150 = 15 items misclassified so far.
The remaining 150-15 = 135 defective items are properly labeled as such.


Of the 850 working items, 0.10*850 = 85 of them are considered "not good" even though they should be considered "good".
The remaining 850-85 = 765 working items are considered "good"


Here's a table summarizing everything
<table border = "1" cellpadding = "5"><tr><td></td><td>Good</td><td>Not good</td><td>Total</td></tr><tr><td>Defective</td><td>15</td><td>135</td><td>150</td></tr><tr><td>Not Defective</td><td>765</td><td>85</td><td>850</td></tr><tr><td>Total</td><td>780</td><td>220</td><td>1000</td></tr></table>
We have 780 items classified in the "good" column. So the proportion of good items is 780/1000 = <font color=red>0.78</font> (i.e. 78% of the items are classified as "good").


Of that total in the "good" column, 15 are defective.


15/780 = <font color=red>1/52</font> is the probability of selecting a defective item if we know 100% it was classified as "good".


1/52 = 0.01923 = 1.923% approximately
Since the decimal and percentage values are approximate, it might be best to stick to the fraction form.



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Summary


Question: <font color=blue>What proportion of the items will be “classified as good”?</font> 
Answer: <font color=red>0.78</font>


Question: <font color=blue>What is the probability that an item is defective given that it was classified as good?</font>
Answer: <font color=red>1/52</font>
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