The Chernobyl and Three Mile Island nuclear accidents cast spotlights on several unresolved safety problems. However, the estimation of radiation health effects has received little attention. There has been considerable research to estimate the probabilities of accidentally bringing the contents of a reactor core into the public domain. This probabilistic risk assessment also involved the estimation of early and delayed health effects. Since delayed cancer and genetic effects are considered to be random, the risk coefficients used in their calculations are given as constants rather that as probable functions. This practice has eliminated consideration of the probability of zero effects, a highly significant probability at low doses for which the coefficients are highly uncertain. As a result, important decisions to be made about nuclear electric power in the United States could have a speculative technical basis.