The family's decision to participate in AFDC-UF is described by a one-period model of utility maximization. The probability of participation is positively related to the level of UF benefits and negatively related to the husband's wage rate, years of school, and to measures of the wife's opportunities for market work. An increase in unemployment insurance benefits, an alternative to AFDC-UF, also reduces the probability of UF participation. Probability estimates are obtained by means of a new statistical technique — maximum likelihood estimation from a choice-based sample. This technique for analyzing choice has wide potential applicability as a low-cost means of extending the range of data suitable for analysis.