#| 

  Card draw problem in Racket/Gamble 

  https://www.reddit.com/r/Probability/comments/1gbm4d0/card_draw_problem/
  """
  I have 100 unique cards. Lets call them card1, card2, card3... etc.
  If i draw 40 cards from the deck what is the chance of me having both card1 and card2 in my hand?
  I asked chatgpt and it said 3.8% but my gut feeling tells me thats way too low.
  Can somone help me out here or is it really 3.8%?
  """


  * importance-sampler (1000000 samples)
  variable : p
  #f: 0.842691
  #t: 0.157309
  mean: 0.157309

  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Racket page: http://www.hakank.org/racket/

|#

#lang gamble

; (require gamble/viz)
(require racket)
(require "gamble_utils.rkt")
; (require "gamble_distributions.rkt")


(define (model)
  (; enumerate
   ; rejection-sampler
   importance-sampler
   ; mh-sampler

   (define n 100)
   (define m 40)

   ;; (define x (sort (take (shuffle (range 1 (add1 n))) m) <))
   ;; ; (define x (sort (draw-without-replacement m (range 1 (add1 n))) <))
   ;; ; (define p (and (= (first x) 1) (= (second x) 2)))
   ;; (define p (equal? (take x 2) '(1 2)))

   ; Faster
   (define x (take (shuffle (range 1 (add1 n))) m))
   ; (define x (draw-without-replacement m (range 1 (add1 n))))
   (define p (if (and (memv 1 x) (memv 2 x)) #t #f))
    
   (list p)

   )
)

(show-marginals (model)
              (list  "p"
                     )
              #:num-samples 1000000
              #:truncate-output 5
              ; #:skip-marginals? #t
              ; #:show-stats? #t
              ; #:credible-interval 0.84
              ; #:hpd-interval (list 0.84)
              ; #:show-histogram? #t
              ; #:show-percentiles? #t
              ; #:burn 0
              ; #:thin 0
              )