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)]
    (transduce (comp (map #(combinations ps %))
                     (map (fn [cs]
                            (transduce
                              (map #(apply ∩-prob %))
                              +
                              cs)))
                     (map-indexed #(* %2 (Math/pow -1 (+ 2 %1)))))
               +
               (range 1 (inc n))
               )))

(∪-prob 0.7 0.5 0.3 0.2)