**41. Flu Outbreak:**
In a community, 8% of people have the flu. A diagnostic test for the flu has a sensitivity of 92% and a specificity
of 95%. If a person tests negative for the flu, what is the probability that they are actually flu-free?
**42. Software Development:**
A software development project has two teams, A and B. Team A has a 75% success rate in delivering bug-free
code, while team B has a 90% success rate. If 60% of the code is developed by team A, what is the probability
that a randomly selected bug-free code was developed by team B?
**43. Book Reviews:**
An online bookstore has two categories of books: fiction and non-fiction. Fiction books receive positive reviews
80% of the time, while non-fiction books receive positive reviews 60% of the time. If 70% of the books are
fiction, what is the probability that a positively reviewed book is non-fiction?
**44. Traffic Signal Failure:**
In a city, 1% of traffic signals malfunction. An alert system correctly identifies 98% of signal malfunctions but
also triggers false alarms for 2% of properly functioning signals. If an alert is received, what is the probability
that the corresponding traffic signal is malfunctioning?
**45. Employee Training:**
A company provides training to its employees to improve their performance. Of the employees who receive
training, 90% show improvement, while 20% of those who don't receive training also show improvement. If
30% of employees receive training, what is the probability that an employee who shows improvement did not
receive training?
