Church solution to the Monty Hall problem

monty-hall.scm

; The Monty Hall problem: can be executed online here: https://probmods.org/play-space.html
(define door-options (list 0 1 2))

(define (random-list-index l)
  (sample-discrete (make-list (length l) (div 1 (length l)))))

(define (filter-out a-list value)
  (filter (lambda (x) (if (equal? x value) #f #t)) a-list))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(define (pick-door)
  (random-list-index door-options))

(define (gen-doors car-door)
  (let [(doors (list 'goat 'goat 'goat))]
    (update-list doors car-door 'car)))

(define (show-door first-choice car-door)
  (if (= first-choice car-door)
      (random-list-index (filter-out door-options car-door))
      (first (filter-out (filter-out door-options first-choice) car-door))))

(define samples
  (mh-query 
   10000 1
   
   (define car-door (pick-door))
   (define doors (gen-doors car-door))
   
   (define first-choice (pick-door))
   (define shown-door (show-door first-choice car-door))
     
   (define switch-doors (flip .5))
     
   (define second-choice
     (if switch-doors
         (first (filter-out (filter-out door-options first-choice) shown-door))
         first-choice))
   
   ; What is the probability that I picked the car door...
   (equal? second-choice car-door)
    
   ; given that I switched?
   switch-doors))

(hist samples "Chance of winning if you switch")

You can run the code here: https://probmods.org/play-space.html