We carry out a large monetary stakes insurance experiment with very small probabilities of losses and ambiguous as well as exact probabilities. Many individuals do not want to pay anything for insurance whether the probabilities are given exactly or are ambiguous. Many others, however, are willing to pay surprisingly large amounts. With ambiguity, the percentage of those paying nothing is smaller and the willingness to pay (WTP) of the other individuals larger than with exact probabilities. Comparing elasticities with ambiguity, we find that worry is much more important than subjective probability in determining WTP for insurance. Furthermore, when the ambiguous loss probability is increased by a factor of 1000, it has almost no effect on WTP. Copyright © 2011 John Wiley & Sons, Ltd.