Answer: About 0.8034 of the items will be classified as good.
Step-by-step explanation:
Let's first understand that because 13% of the items are defective, that means 87% of the items are not defective. And because the inspector incorrectly classifies the items 9% of the time, it's important to understand that that means both the defective and the not defective items may be incorrectly classified. In order to figure out what proportion will be classified as 'good,' let's set up a tree diagram:
--0.13--defective
|__0.09__ classified as 'good'
|__0.91__ classified as 'defective'
--0.87--not defective
|__0.09__ classified as 'defective'
|__0.91__classified as 'good'
This chart essentially reiterates the information in the prompt, showing that 9% of each type of item will be incorrectly classified. Now we need to find the proportion of items that will be classified as 'good.' To do this, we must multiply the proportion of items classified as 'good' by the proportion of items that are either defective or not defective for both types, like this:
(0.13 * 0.09) + (0.87 * 0.91)
this expression in words means: "13% of the items will be classified as good 9% of the time, and the other 87% of the items will be classified as good 91% of the time"
When we multiply and add these numbers together, we get 0.8034, but you should round to 2 or 3 decimal places like the prompt instructs. Hope this helped! :)
