Inclusion–Exclusion Principle for probabilities in Clojure.

∪_prob.clj

(require '[clojure.math.combinatorics :refer [combinations]])

(defn ∩-prob
  [a & more]
  (reduce * a more))

(defn ∪-prob [a b & more]
  "https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle#In_probability"
  (let [ps (concat [a b] more)
        n (count ps)]
    (loop [k 1 prev 0]
      (if (> k n)
        prev
        (let [pow (+ k 1)
              mult (Math/pow -1 pow)
              cs (combinations ps k)
              intersections (map #(* mult (apply ∩-prob %)) cs)]
          (recur (inc k) (reduce + prev intersections)))))))

(∪-prob 0.7 0.5 0.3 0.2)