Nuclear math Wikipedia

These numbers, from Wikipedia, may help:

• There are 442 nuclear plant units around the world.
• There are 139 in the U.S.
• There have been 99 nuclear plant accidents
• 56 of these have occurred in the U.S.
• There have been 57 since Chernobyl (1986) 

So, roughly speaking, based on these numbers, there is about a 20% chance of an accident (not necessarily a serious one) at a nuclear plant.

• There is a 40% in five chance of an accident (not necessairly serious) at an American nuclear plant.
• These numbers are extremely rough. For example, they don't take into account when the plants were built or distinguish between severity of accidents.
• But it does suggest that nuclear power lacks the level of safety many politicians and advocates have claimed on its behalf.

Further, current discussions seem to overlook this information about nuclear waste, as noted by Wikipedia:
...Nevada ranks fourth in the nation for current seismic activity. Analysis of the available data in 1996 indicates that, since 1976, there have been 621 seismic events of magnitude greater than 2.5 within a 50-mile radius of Yucca Mountain...

    In June 2008, a major nuclear equipment supplier, Holtec International, criticized the Department of Energy's safety plan for handling containers of radioactive waste before they are buried at the proposed Yucca Mountain dump. The concern is that, in an earthquake, the unanchored casks of nuclear waste material awaiting burial at Yucca Mountain could be sent into a "chaotic melee of bouncing and rolling juggernauts"... TPR