What I've done so far....
We expected he would get $15$ right, so now those $15$ are definitely wrong. So there are 5 he could potentially get right, but he only has a $1/10$ chance of getting each one right. So his expected value is $0.5$ points, which would be $0.025%$ on the exam...this just feels intuitively wrong but I can't put my finger on why. I feel it has something to do with variance in the first step but not sure how to incorporate that. Any help is very appreciated.