I have this statistics question. I have never done the like before. could you plz explain it to me

"A fair dice is thrown twice. If the second score is the same as the first, the second throw does not count, and the dice is thrown again until a different score is obtained. The two different scores are added to give a total.

List the possible outcomes.

Find the probability that
a) the total is 7,
b) the total is at least 8,
c) at least one of the two scores is a 6,
d) the first score is higher than the last."

What I don’t understand is how to deal with this part: “If the second score is the same as the first, the second throw does not count, and the dice is thrown again until a different score is obtained.”

The answer I get for a) eg is 1/6*1/6*6=1/6 but it’s not correct cux obviously this statement plays a part in the solution. But the tree diagram could continue forever with this statement considered. Cux we are never ‘sure’ when we wouldn’t need to take further throws. The answer for instance to part a) is 1/5. How is that?

a) ignore the sentence "“If the second score is the same..."
we have 30 states, {all of the cases except the pairs} and we only want {(6,1),(1,6),(5,2),(2,5),(4,3),(3,4)}. then the answer is 6/30 or 1/5 or 0.2.
b) again ignore. we calculate the cases for 8 {(2,6)(6,2)(3,5)(5,3)} the cases for 9 {(6,3)(3.6)(5,4)(4,5)} the cases for 10 {(6,4),(4,6)}, the cases for 11 {(6,5),(5,6)} and the cases for 12 {no cases}
then the answer is 12/30.
c)we have these cases {(1,6)(2,6)(3,6)(4,6)(5,6)(6,1)(6,2)(6,3… then the answer is 10/30.
exactly 1/2 or 0.5.
because we have only two cases, bigger and smaller.
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