ball-swapping-simulation.clj

(defn replace-values 
    [array current-value new-value]
    (assoc array (.indexOf array current-value) new-value))

(defn swap-balls-in-boxes
    [box-a box-b]
    (let [random-ball-a (rand-nth box-a)
          random-ball-b (rand-nth box-b)]
        [(replace-values box-a random-ball-a random-ball-b)
         (replace-values box-b random-ball-b random-ball-a)]))

(defn simulation
    []
    (let [box-a ["white"]
          box-b ["white", "black"]]
        (->> [box-a box-b]
             (apply swap-balls-in-boxes)
             (rand-nth)
             (rand-nth))))

(defn avg-of
  [n coll]
  (float (/ (count coll) n)))

(defn white-ball-probability
    [n-simulations]
    (->> (repeatedly simulation)
         (take n-simulations)
         (filter #(= % "white"))
         (avg-of n-simulations)))

(white-ball-probability 100000)  ; should be 0.625 on average