Dice probability Question

Hi There!

This is my first time posting on this forums, so I hope im following the right etiquette.

Im having some severe difficulties with the problems under Question 3 in this past exam paper. http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2014/91267-exm-2014.pdf
Can someone please check my answers and explain the questions where I faceplanted? Thanks

3. (a), I got 1/9 which im pretty sure is good.
3. (b), I got 2/3 which im pretty sure is good.
3. (c,i). I got 1/81, im not very confident about this answer because the wording of the question is incredibly bad. I did 4/36 X 4/36 as that's the probability he gets 5 on the first roll, and then 5 on the second roll to win?
3. (c,ii). I got 13/1458, I don't think I got this right because it seems like such a crazy probability. I did the probability he got the sum of 5 on the first roll (4/36), multiplied by the probability that he did not get a sum of 5 on the second roll (13/18 I think??? I might be wrong), the multiplied again by the probability that he will get a sum of 5. so in total (4/36 X 13/18 X 4/36 = 13/1458)???? Really confused about this question.
3. (d) This question I had absolutely no idea what to do. I some how got 7/18, but I think im wrong.

Thanks so much!

For those who don't want to have to plow through a lengthy document which may soon go offline, here is the question:

QUESTION THREE

Matiu and Whiti are playing a game with two fair six-sided dice numbered 1 to 6.

Matiu starts by rolling the two dice together.
If the sum of the numbers showing on the dice is 7 or 11, then Matiu wins the game.
If the sum of the numbers showing on the dice is 2, 3, or 12, then Matiu loses the game.
The table below shows the probability for each possible sum of the numbers showing on the dice.

Probabilities of the sum of the numbers showing on the dice:


(a) What is the probability that Matiu loses on the first roll?

(b) What is the probability that there is no winner on the first roll?

(c) If neither Matiu nor Whiti wins the game on the first roll (the sum of the numbers showing on the dice is not 2, 3, 7, 11, or 12), then the actual sum of the numbers showing on the dice that Matiu has thrown on this first roll becomes Matiu's target score for the rest of that game. Matiu keeps rolling the dice until either the sum on the dice is his target score, or he rolls a sum of 7, whichever occurs first. Whiti does not roll the dice. If Matiu's target score occurs first, he wins; if a 7 occurs first, then Whiti wins. Suppose Matiu gets a sum of 5 on the first roll.

(i) What is the probability Matiu will win the game on the second roll?
(ii) What is the probability Matiu will win the game on the third roll?

(d) Matiu and Whiti modify the game. They want the modified game to be fair and to finish after a maximum of two rolls.

First roll:
sum is 2, 3, or 12: Whiti wins
sum is 7 or 11: Matiu wins
sum is anything else:

Second roll:
Matiu wins
Whiti wins

To the reader: There are no "rules" given for the second roll, just the two outcomes.