In response to stimulation, B lymphocytes pursue a large number of distinct fates important for immune regulation. Whether each cell's fate is determined by external direction, internal stochastic processes, or directed asymmetric division is unknown. Measurement of times to isotype switch, to develop into a plasmablast, and to divide or to die for thousands of cells indicated that each fate is pursued autonomously and stochastically. As a consequence of competition between these processes, censorship of alternative outcomes predicts intricate correlations that are observed in the data. Stochastic competition can explain how the allocation of a proportion of B cells to each cell fate is achieved. The B cell may exemplify how other complex cell differentiation systems are controlled.