Probability — practice question

A standard fair $6$-sided die is used in a game. The player rolls once. If the outcome is $2$, $3$, $4$ or $5$, that number becomes the score and there is no second roll. If the outcome is $1$ or $6$, the player rolls again and the score is the total of the two results from the two rolls. Events $A$ and $B$ are defined as follows. $A$: the player's score is $5$, $6$, $7$, $8$ or $9$. $B$: the player has two throws.