With the first question:
You will need to create the probability distribution table for the recorded score (just like I suspect you did for (a)).
For example, to get a recorded max score of 5 the student may have got:
0 then 5..... P(0,5) =0.06 or
5 then 0 …..P(5,0) =0.04 or
5 then 5 ….P(5,5) = 0.15
So add these to get P(max score = 5)
Do the same for the other possible maximums to generate your prob dist table.
(Double check that your p's add to 1)
Then find the expected value in the usual way.