In a game of craps a player throws a pair of dice The game e

In a game of craps, a player throws a pair of dice. The game ends with the first throw if a 2, 3, 7, 11 or 12 is thrown. Otherwise, the player throws the dice repeatedly until either the number obtained on the first throw occurs again or a 7 is thrown. Where is the expected number of throws to complete the game?

the answer is 3.3758 but I just dont know how

Solution