People are more willing to pay for insurance against low-probability disasters when the risks are ambiguous rather than known, due to greater worry about ambiguous risks. An experiment measured people's willingness to pay for insurance covering risks ranging from 1 in 5,000 to 1 in 5. It found that willingness to pay was higher and fewer people refused to pay anything when risks were ambiguous rather than precisely defined. Worry had a greater impact on willingness to pay than subjective probability estimates for small-probability risks. Changing the risk level by a factor of 1,000 had no significant effect on willingness to pay.