**26. Population Health:**
In a certain town, 8% of the population has a rare health condition. A diagnostic test for the condition has a
sensitivity of 92% and a specificity of 95%. If a randomly selected person tests positive for the condition, what
is the probability that they actually have it?
**27. Software Bugs:**
A software program has a bug that causes it to crash in 2% of its executions. The program also crashes
randomly with a 1% probability when there is no bug. If the program crashes, what is the probability that the
bug is the cause?
**28. Job Applicant Screening:**
A company is hiring for a position, and 10% of the applicants are qualified. The HR department has a screening
process that correctly identifies 80% of qualified applicants but also rejects 5% of unqualified applicants. If an
applicant is rejected, what is the probability that they were unqualified?
**29. Online Shopping Cart Conversions:**
An e-commerce website has two versions of its checkout process. Version A has a conversion rate of 5%, while
version B has a conversion rate of 8%. If 60% of users go through version A and 40% through version B, what is
the probability that a randomly selected user who made a purchase went through version B?
**30. Classroom Participation:**
In a classroom, 15% of students actively participate in discussions. A teacher randomly selects a student who
participated and finds out that the student did their homework with a probability of 70%. If a student did not
participate, what is the probability that they did not do their homework?
