That was my answer as well: My reasoning: Let x be the probability of purchasing disability coverage, thus the probability of purchasing collision is 2x from conditions b and c, we know that 2x∙x = .15 so we can calculate the probability of neither applying as 1-(2x+x)+2x∙x = .18 + .15 = .33

I can see the trap of forgetting to add 2x∙x in the calculation (since we don't want to double count the case where they purchase both insurances). And choices d and e follow from forgetting to subtract the probability of purchasing either from 1 (and making the same mistake of not removing the double count). I'm curious where the .48 distractor comes from. Coming up with good distractors is the secret to making a multiple choice test hard (students tend to think that multiple choice will be easier than a fill in the blank test, but they forget that with free answer exams, they can still get partial credit where in a multiple choice test, they'll lose all credit for a small mistake).

> with free answer exams, they can still get partial credit

Rarely had a prof that had the patience for that, vs. a simple red X. Not arguing, it's just my anecdote of frustration.

I taught a lot of high school/junior high math for college students back in the day and typically the midterm exams and quizzes would get partial credit and the final was multiple choice. We had very specific rubrics for partial credit grading and this was typical of the classes that I took as well.