When there is little information on which probabilistic assessments are based, we cannot expect precise results. To avoid a false impression of accuracy and confidence, the degree of uncertainty must be explicitly seen in the resultant assessments on which decisions are based. In the approach described in the paper, probability assessments are interval-valued, and the width of the interval reflects the amount of information on which probabilities are based. As more data become available, the interval becomes narrower. Updating the interval-valued probabilities is performed with the imprecise beta-Bernoulli model which is described in the paper. An example on calculating the probability of failure of a component with the Bayesian approach and the beta-Bernoulli model is provided.