**11. Faulty Manufacturing:**
In a factory, 2% of produced items are faulty. A quality control test catches 95% of faulty items but also
misidentifies 3% of non-faulty items as faulty. If an item fails the quality control test, what is the probability
that it is actually faulty?
**12. Website Conversion Rates:**
A company is testing two versions of its website to see which one has a higher conversion rate. Version A has a
conversion rate of 10%, while version B has a conversion rate of 15%. If 60% of users see version A and 40% see
version B, what is the probability that a randomly chosen user who made a purchase saw version B?
**13. Car Accident Investigation:**
In a certain area, 1% of drivers are involved in hit-and-run accidents. The police have a witness who correctly
identifies the fleeing driver 80% of the time. If a driver is involved in a hit-and-run accident, what is the
probability that the witness correctly identifies them as the culprit?
**14. Online Ad Click-Through Rates:**
An online advertising campaign has two different ad designs. Ad A has a click-through rate of 3%, while ad B
has a click-through rate of 5%. If 70% of users see ad A and 30% see ad B, what is the probability that a user
who clicked on an ad saw ad B?
**15. Student Performance:**
In a class, 10% of students did not study for an exam and are expected to fail. However, even among the
students who did study, there's a 5% chance of failing. If 20% of students did not study, and you randomly
select a failing student, what is the probability that they did not study?
