Humans have the ability to reason. You can look at a situation and take what knowledge you have of it in the present and combined with the history of the situation you can make predictions.
Previously the Fukushima Daiichi nuclear disaster was discussed. A nuclear power plant was essentially breached by a tsunami caused by a massive earthquake. Could this have been predicted? It is not as if Japan has never had an earthquake, or that a tsunami is so rare as to be inconsequential when considering where to build a nuclear facility. Additionally, what types of design features are needed if you consider the worst-case scenario? What is needed in the worst-case scenario to protect the material used for nuclear power? Who failed to assess and then decided on the worst-case.
Think about the people who work at the nuclear facilities in your state or even in your community. You would assume and rightly so, that they are vetted and that someone is looking over their shoulders at all times. You would assume but based on past events, your assumptions may be wrong. Once again, you have to use what knowledge you have now and take what has happened in the past to determine whether there is a possible threat in your community and state and if there is, what precautions you can take. Facts and history are your tools for making informed decisions.
Anything can happen at any time to anyone but how likely are some threats, and are there measures that can be taken to prevent or protect you and your family? Unfortunately, you cannot prevent most things from happening; you can only react after the fact.
You cannot possibly prepare for anything and everything, so you have to prepare for the most likely. Generally, preparedness is not disaster specific unless you live in the shadow of a nuclear facility. You have to look at distance, time, and extent. In other words how far away do you live from a site and if it was to fail and there was a meltdown, ask yourself, do you have time to evacuate the area. In the short-term, you have to assume the worst so severity should only be assessed after you have evacuated far enough away to where radiation fallout would not be a factor.
Do you live in an earthquake prone area with a reactor close enough to cause a problem if a massive earthquake were to happen? Do you live on the coast where a tsunami would cause problems? Because one can happen essentially at any time from an earthquake hundreds of miles away in the middle of the ocean.
The authorities would never tell you it is a possibility because of the additional costly measures. Citizens are always left wondering until something happens and then there is a history, then comes knowledge and then you can predict what might happen in the future.