Church

(define (sample-coin weight num-flips)
  (if (= num-flips 0)
      '()
      (cons (if (flip weight) 'h 't)
            (sample-coin weight (- num-flips 1)))))

(define (count-heads lst)
  (if (null? lst)
      0
      (+ (if (eq? (first lst) 'h) 1 0)
         (count-heads (rest lst)))))

(define (coin-model observed-heads num-flips)
  (rejection-query
    (define fair-weight 0.5)
    (define biased-weight 0.9)
    (define is-fair (flip 0.5))
    (define weight (if is-fair fair-weight biased-weight))
    (define flips (sample-coin weight num-flips))
    (define heads (count-heads flips))
    is-fair
    (= heads observed-heads)))

(define num-samples 1000)
(define num-flips 10)
(define observed-heads 8)

(define samples
  (repeat num-samples
    (lambda () (coin-model observed-heads num-flips))))

(define fair-count
  (length (filter (lambda (x) x) samples)))

(display "Probability coin is fair given ")
(display observed-heads)
(display " heads in ")
(display num-flips)
(display " flips: ")
(display (/ fair-count num-samples))
(newline)