As an ice-breaker on the first day of analytics class with 25 students in attendance, a professor announces that a free textbook will be awarded to any students who share a birthday (month and day, not necessarily same year). Assume the probability of any student being born on any particular day is 1 in 365 (neglecting leap years).

a. Construct a simulation model to estimate the probability that there is at least one pair of students sharing the same birthday.

b. What is a 95% confidence interval on the probability provided in part (a)?