Accidents can and do happen.
We can (or at least should) always assess the risk before any trip and plan for reasonably foreseeable eventualities. We also must (or at least should) accept that there is always a chance (often down to luck) that we will have an accident and could die as a result. We take precautions to reduce this risk, but the risk remains nonetheless.
Risk is generally considered to be a combination of two things:
1. the likelihood of something bad happening;
2. the consequence if that bad thing does happen.
Humans are instinctively very good at understanding consequence; if something might kill us, we are very wary of it. What comes less naturally is assessing likelihood.
About this time last year, I heard an interesting discussion on the radio with a researcher, who presented this very well. In her study, participants were presented with a machine that could give them an electric shock and asked how much they would need to be paid to touch it.
There were a number of scenarios presented to different groups. The first two groups were told that the shock would be a light shock (similar to a pinch); one group was told that there was a probability of 1 in 10 that they would get a chock, the second group told that there was a probability of 1 in 100 that they would get a shock.
The second two group were given the same two probabilities, but told that the shock would be like a thump, that would give them a dead arm.
Both the first two groups asked for about ?1 to touch the machine (regardless of the 1:10 or 1:100 probability). Both of the second two groups asked for close to ?10 to touch the machine; the group with the higher probability did on average ask for a little more, but very comparable.
What this shows us is that when assessing the risk, participants had a good idea about the consequence, but that they paid virtually no attention at all to the likelihood. 10 times more chance and there was virtually no change to the response.
As part of my job, I am required to assess risk in construction; specifically, the risks that are introduced while designing something. At an early stage, we identify how our proposals could present a risk when being built or maintained. We then look at how to mitigate that, either by reducing the consequence (eg reducing the height of an exposed drop), or by reducing the likelihood (eg providing a handrail next to an exposed drop). When I review designers risk assessments, it is amazing how many professional engineers and architects fail to understand risk. They can usually identify a risk, then even introduce design mitigations to reduce it, but more often than not, they fail to understand whether those measures reduce consequence or likelihood.
The other thing people struggle with is frequency. If an activity carries a 1 in 1,000 chance of an accident, that might be ok as a one-off, but if you had to do that activity once a day at work, an accident would probably happen once every 4 years. If you employed 100 people doing that activity, an accident would probably happen every 10 days, so you would probably want to think about some control measures to either eliminate the risk (where possible), or otherwise reduce the likelihood, or consequence.
In the context of caving, the only way to eliminate risks is to not go caving at all, so instead we need to take steps to reduce likelihood of an accident (eg using P-hangers instead of spits or thoroughly checking your equipment before any trip) and to reduce the consequence if an accident does occur (eg backing up an anchor, carrying 1st aid equipment).
Sometimes there is a trade-off; more people on a trip increases the chance of an accident (more frequency), yet it may reduce the severity if an accident does occur (others on hand to help). The balance will depend on the nature of the cave and the individuals involved; a good example would be the difference in approach between UK and US cave diving. The former is predominantly considered safer solo due to cave conditions, the latter is more often considered safer with a buddy.
It's definitely not a precise science, but the better we all understand the combination of likelihood, as well as consequence, the better equipped we all are to keep ourselves safe, while still doing the things we enjoy, even if they carry a risk of death or serious injury.