**36. Product Defects:**
In a manufacturing plant, 4% of products are defective. A quality control test correctly identifies 90% of
defective products but also falsely flags 3% of non-defective products. If a product is flagged as defective, what
is the probability that it is actually defective?
**37. Network Security:**
A network security system has a detection rate of 98% for identifying malicious activities and a false positive
rate of 1%. If 0.5% of network activities are malicious, what is the probability that an alert triggered by the
system is for a legitimate threat?
**38. Job Interviews:**
In a company, 15% of job applicants are qualified for a position. The HR department correctly identifies 80% of
qualified applicants but also mistakenly rejects 10% of unqualified applicants. If an applicant is accepted, what
is the probability that they are qualified?
**39. Traffic Accidents:**
In a city, 2% of drivers are involved in accidents on a given day. A traffic camera system correctly captures 95%
of accidents but also records 3% of non-accident events as accidents. If a recorded event is flagged as an
accident, what is the probability that it is a genuine accident?
**40. Online Survey Responses:**
An online survey has two versions, A and B. Version A has a response rate of 20%, while version B has a
response rate of 15%. If 60% of users see version A, what is the probability that a randomly selected
respondent who completed the survey saw version B?
