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;; Monty Hall problem (Let's Make a Deal gameshow)
;; http://www.marilynvossavant.com/articles/gameshow.html
(use '(incanter core stats charts))
;; set a simulation sample size
(def n 10000)
;; generate samples of initial-guesses, prize-doors, and switch decisions
(def initial-guesses (sample [1 2 3] :size n))
(def prize-doors (sample [1 2 3] :size n))
(def switches (sample [true false] :size n))
;; define a function that returns 1 if a switch decision results in winning
(defn switch-win? [initial-guess switch prize-door]
(if (and switch (not= initial-guess prize-door)) 1 0))
;; define a function that returns 1 if a stay decision results in winning
(defn stay-win? [initial-guess switch prize-door]
(if (and (not switch) (= initial-guess prize-door)) 1 0))
;; calculate the joint probability of winning and switching
(def prob-switch-win (/ (sum (map switch-win?
initial-guesses
switches
prize-doors))
n))
;; calculate the probability of switching doors
(def prob-switch (/ (sum (indicator true? switches)) n))
;; calculate the conditional probability of winning given a switch
(def prob-win-given-switch (/ prob-switch-win prob-switch))
;; calculate the joint probability of winning and NOT switching
(def prob-stay-win (/ (sum (map stay-win?
initial-guesses
switches
prize-doors))
n))
;; calculate the probability of NOT switching doors
(def prob-stay (/ (sum (indicator false? switches)) n))
;; calculate the conditional probability of winning given NOT switching
(def prob-win-given-stay (/ prob-stay-win prob-stay))
(view (pie-chart ["Switch" "Stay"]
[prob-win-given-switch prob-win-given-stay]))
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