hackerrank binomial-distribution-1

{-
binomial-distribution-1: https://www.hackerrank.com/challenges/binomial-distribution-1/
  Author: Evgeniy Malov <[email protected]>
  Date: Jan 4, 2025
  join me : https://www.youtube.com/@EvgeniyMalov
            https://ru.linkedin.com/in/deepwalk            
-}

import Text.Printf (printf)
-- 4 shots
-- more than 2 hits - it is equal to 
-- A  - event of 3 or 4 hits
-- P(A) = ?
-- B = 1 miss
-- P(A) = 1 - P(B) = ?

-- at least 3 misses
-- A - 3 or 4 misses
-- B - 1 hit or 0 hits
-- P(A) = 1 - P(B)

-- P(K) = C(N,K)*P^K*Q^(N-K)

fac 0 = 1
fac n = n*(fac $ n - 1)

cnk k n = (fac n) `div` ( (fac (n - k)) * fac (k))

binp n k p = (fromIntegral (cnk k n)) * (p ^ k) * ((1 - p)^(n-k))

p :: Double

p = 4 / 5
p1 = binp 4 3 p + binp 4 4 p 
p2 = binp 4 1 p + binp 4 0 p

main = do
        printf "%.3f\n" p1
        printf "%.3f" p2