Yes, I believe you are correct. The person can either die from the occupational hazard or all other causes. As the rates are independent, the probability of the person surviving would be the probability of not dying to the occupation hazard multiplied by not dying to the other causes, resulting in your expression.
As for the amount of work for 4 marks, I don't think so? The working can take some time but that is the nature of contingencies. Finding the most efficient way to calculate is the key really (which I would say try and store values in your calculator so it saves you time). But what I think about this doesn't really matter at all. What matters is the person who sets the question and how they feel about the number of workings for the number of marks awarded. Clearly this examiner felt it was fair so we must give it our best answer and go from there.
A small tip on this subject from when I wrote this subject through the board is that often the time pressure is so intense that you actually don't have time to get to the answer. I found that just leaving out the final answer if I was running low on time for the question saved me enough time to properly answer everything and can be a useful tactic to getting more marks in the exam (if you don't struggle for time, then you have nothing to worry about but if you are like me then it's a great way to sacrifice half a mark to gain 1-1.5 marks in another question). And if you have time at the end you can go back, manually enter the past parts of the question in your calculator and calculate the final answer. The key to this is to have a solid time-management strategy and stick to it.
I used a 1.8 minutes per mark approach and would calculate the exact time I then had to finish the question. If I was till working on the question as the time limit was hit, I moved on. Just meant I could get all the marks I needed to get the exemption because I could spend an appropriate amount of time on each question. It takes a little practice and there are tons of other methods out there, but find the one for you and go for it (another method includes 1.5 minutes per mark leaving extra time at the end).