As is well known, the positron was discovered in August 1932 by Carl Anderson while studying cloud chamber tracks left by cosmic rays. Far less known is the fact that a few months before Anderson's discovery, in April 1932, Frederic Joliot and Irene Curie had missed an opportunity to discover the positron during a nuclear physics experiment. One year later, in April 1933, the French researchers eventually succeeded in discovering the mechanism of positron-electron pair production. The complex relationship between Anderson's discovery of the positron, Joliot and Curie's missed discovery, and their following work on the pair production is discussed here in detail. (Contains 3 footnotes and 6 figures.)