Birthday Problem

What is the probability that in a room filled with 23 people, at least one pair of people has the same birthday?

(define N 23)

(define (two-birthdays-match?)
  (rejection-query
   
   (define birthday 
     (mem (lambda (i) (+ (sample-integer 365) 1))))
   
   (define (pair-equal i j)
     (if (> i N) 
         false
         (if (> j N)
             (pair-equal (+ i 1) (+ i 2))
             (if (= (birthday i) (birthday j)) 
                 true
                 (pair-equal i (+ j 1))))))
   
   (pair-equal 1 2)
   
   #t))

(hist (repeat 1000 two-birthdays-match?))