The following question was inspired by recent comments to the post on Elchanan Mossel’s amazing Dice Paradox.
A fair dice is a dice that when thrown you get each of the six possibilities with probability 1/6. A random dice is such that you get the outcome ‘k‘ with probability 
Test your intuition:
You throw a random dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers?
