The number of calls in a telephone survey is used as an indicator of how difficult an intended respondent is to reach. This permits a probabilistic division of the non-respondents into non-susceptibles (those who will always refuse to respond), and the susceptible non-respondents (those who were not available to respond) in a model of the non-response. Further, it permits stochastic estimation of the views of the latter group and an evaluation of whether the non-response is ignorable. These ideas are implemented on the data from a survey in Metropolitan Toronto of attitudes toward smoking in the workplace. Using a Bayesian model, the posterior distribution is sampled by Markov Chain Monte Carlo methods. The results reveal that the non-response is not ignorable and those who do not respond are twice as likely to favor unrestricted smoking in the workplace as are those who do.