The standard BtS chance for a meltdown is 1 in 2000. That is per turn for each of them. It is not done through the random event system so it can still happen even if you have random events turned off.
With 5 of them for 30 turns you have under an 8% chance of having at least one have a meltdown - it is just under 92.8% to not have any. If you have 6 for 35 turns the odds of no meltdown go down to just a hair over 90%. If you put them in more cities (or have them for longer) it gets worse: with 20 cities for 30 turns the odds are only a bit over 74% that you will not have at least one meltdown in that time. The same 20 cities for twice as long, 60 turns, drops the odds of no meltdowns to under 55% and if you and 25 instead of 20 then it is below 50% (about 47.2%) for no meltdown.
The odds are low, but the consequences are devastating. It is identical to having a nuke dropped on the city. Nuking your own city is not a good plan. It will destroy many buildings, reduce the population, spread some fallout around the city, damage every unit in the city (possibly killing some). It would not be a surprise of it takes 50 turns to get the city back to where it was just from the time it takes to rebuild all the buildings. If you don't already have the tech to scrub fallout, it is that much worse since you'll be rebuilding without the possibility of using some of the city's plots.
A small number of nuclear plans in minor cities is not likely to be much of a problem (having some tundra city built just to claim a resource have a meltdown is not much of a problem). Putting them in your major cities and/or a lot of cities is just asking for trouble.
Coal comes first, which is itself an advantage. If built in the same city, nuclear replaces coal and removes the 2 extra unhealth but adds the chance of a meltdown. Hydro will replaces coal and/or nuclear removing both the unhealth from the coal and the meltdown chance from the nuclear. Hydro is the best, but it comes later and requires the city to be on a river. Nuclear is the worst - the only advantage over coal is two less unhealth which may let you have one more population in the city, as long as you don't mind killing them up later when the thing melts down...