During the 1980s and 1990s, the quantity of probability being taught in mathematics lessons in primary schools in England and Wales went from minimal to extensive and back again. A great deal of effort was invested in a project to incorporate probability into the primary curriculum that has now almost been abandoned. In this article I will attempt to explain this by considering the probability experiences that primary children had, in relation to the hopes for learning that the curriculum contained. I shall argue that what was done did not lead to mathematical learning because in most cases it was not mathematical experience. One consequence of this was that primary aged children did not learn anything about probability that could be reliably assessed, and so probability as a curriculum component did not contribute to some of the purposes of the National Curriculum.