Performance based assessments of statistical thinking provide teachers with a window to students' conceptual development. With this aim in mind, we examined the performance of a pair of fourth/fifth-grade students working collaboratively on a probabilistic assessment task developed by the California Department of Education. To account for student performance, we developed a cognitive model of the knowledge guiding student performance. Using this cognitive model, we revised the assessment to provide opportunities for assisted performance. We believe that performance assessments of statistical thinking should be designed with ways to assist performance, a view consistent with visions of teaching and learning as assisted performance.