Dawn of the planet of Apes

Discrete Mathematics Level 3

Its dawn of the planet of apes and somehow an ape got into an armed spaceship. He is trying to launch a missile by clicking random buttons on the board.

There are three buttons on the board: \((R)Red\), \((G)Green\) and \((B)Blue\). A missile will be launched if the ape presses Red, Green, Blue consecutively in sequence. What is the expected number of missiles that he will launch if in total he pressed \(1000\) buttons while in the spaceship?

Choose the closest integer as your answer.


Suppose he pressed the following buttons in sequence: \(R, G, B, B, G, R, G, B, B\), then \(2\) missiles will be launched.


  1. Assume the ape is not capable of learning.
  2. He presses the buttons equally likely
  3. He doesn't break the buttons while pressing.

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