Two schools A and B can admit a maximum of 420 students. 800 candidates want to enroll in both schools. Each candidate chooses which school they will go to with a probability of 1/2.

a) Calculate the approximate probability that none of the schools will run out of places. b) Find the smallest number of N places prepared by each school so that with the selection procedure described above there will be no shortages of places in any of the schools with a probability of 0.99.