## Venn Diagram Question

In testing an automatic inspection device for detecting defective items, an experiment was set up as follows: 1000 items, of which 100 were true defective, were run trough the device. The device indicated 105 of the items defective of which 90 were found to be true defectives. The items were then run through the device again. This time the device indicated 103 to be defective including 3 of the true defectives it missed before, 85 of the true defectives it caught before, and 4 of the items it falsely indicated to be defectives before.

1. Make a Venn Diagram showing the eight classes
2. How many items were indicated as defectives at least once by the device?
3. If an item is truly defective, what is the probability that it will be caught if it runs through the device once?
4. What is the probability that a good item will be indicated as defective if it runs through the device once?

Please help! If someone could break this down step by step for me that would be amazing. Thank you!