A board game consists of four positions labeled A, B, C, and D. Whenever you reach position A or B, you roll some dice whose results determine what position you will move to next. Ah, but these dice are loaded.

**From** position A, there is a 1/4 chance of

**moving to** position B, a 1/12 chance of

**moving to** position C, and a 1/6 chance of

**moving to** D.

**From** position B, there is a 1/3 chance of

**staying** at B, there is a 1/3 chance of

**moving to** position A, a 1/6 chance of

**moving to** position C, and a 1/6 chance of

**moving to** D.

Whenever you reach position C or D the game is over and you win some cake.

Suppose you begin the game at position A, what is the probability you end the game at position C