Probability question

I can't seem to get the correct answer for this probability question:

Seven identical balls are marked respectively with the numbers 1 to 7 inclusive. The number on each ball represents the score for that ball. The seven balls are then put into a bag. If two balls are chosen at random one after the other, find the probability of obtainting a total score of 11 or more

(a) if the first ball is replaced

(b) if the first ball is not replaced

I could do these.

Then there is a bit at the end which says:

If 2 balls are chosen at random one after the other from the 7 balls, find in case (a) and in case (b) the most probable total score for the 2 balls with its associated probability.

I can do the bit on a) as getting a total score of 8 has the greatest probability according to my diagram, which is 1/7, but I don't know how to do it for part b). The answer is 7,8,9 -> 1/7, but I can't see how they got this.

Thanks