In a poker game you receive five cards (no jokers in the game). What is the probability of getting Full-House, which is two of a kind and three of kind, in the first hand (Example 2 Aces and Three Queens)?

If by the ellipses you mean to say that the number 7 repeats forever after that point, then it is not irrational. Any number which can be expressed with repeating decimals is not irrational. For example, pi is an irrational number because it has no repeating decimals, but 0.33333333... is not irrational because it can be expressed by simply saying 0.3 repeated.