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$2$. $8865$ Specimen Paper Q$7$$\newline$A game is played with a fair $6$-sided die. A player throws this die, and if the result is $2,3,4$ or $5$ that result is the player's score. If the result of the player's throw is $1$ or $6$ , the player throws second time and the score is the sum of the two numbers from the two throws. Events $A$ and are defined as follows:$\newline$$$5: 123456789$$$\newline$$A: \quad$ the player's score is $5,6,7,8$ or $9$ ,$\newline$$B: \quad$ the player has two throws.$\newline$(i) Draw a tree diagram to represent this situation, showing all possible outcomes.$\newline$$[2]$$\newline$(ii) Show that $\mathrm{P}(A)=\frac{1}{3}$.$\newline$(iii) Find the probability that a player gets a score of $5$, $6$, $7$, $8$ or $9$ in two throws.$\newline$(iv) Describe what is meant by the probability $\mathrm{P}(A \mid B)$ in this context and find its value. [$3$