yaworsw/euler-manager

---
:id: 329
:name: Prime Frog
:url: https://projecteuler.net/problem=329
:content: "Susan has a prime frog.  \nHer frog is jumping around over 500 squares
  numbered 1 to 500. He can only jump one square to the left or to the right, with
  equal probability, and he cannot jump outside the range [1;500].  \n(if it lands
  at either end, it automatically jumps to the only available square on the next move.)\n\nWhen
  he is on a square with a prime number on it, he croaks 'P' (PRIME) with probability
  2/3 or 'N' (NOT PRIME) with probability 1/3 just before jumping to the next square.
  \ \nWhen he is on a square with a number on it that is not a prime he croaks 'P'
  with probability 1/3 or 'N' with probability 2/3 just before jumping to the next
  square.\n\nGiven that the frog's starting position is random with the same probability
  for every square, and given that she listens to his first 15 croaks, what is the
  probability that she hears the sequence PPPPNNPPPNPPNPN?\n\nGive your answer as
  a fraction p/q in reduced form.\n"