The director of the library calculates that 29% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4%? Round your answer to four decimal places.

Each person in an it department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. how many people work on system security and program implementation?