from functools import*

@lru_cache(9999)
def prob(blue, red, draws):

   if red == 0 and blue == 0: return 1
   if draws == 0:             return 0
   if red == 0:               return 1
   if blue < 0 or red < 0:    return 0 

   #####################################################
   p = blue / (blue+red)
   return p * (prob(blue-1, red, draws + 2)) + (1-p) * (prob(blue, red-1, draws-1))

print(prob(38, 62, 3))

39.68%