Consider someone who sets out to collect data sequentially in such a way as to disprove a hypothesis,H0, about the value of θ, the mean of a normal distribution. Observation is continued as long as the posterior probability ofH0exceeds α1and stopped when it falls below it. It is shown that if a non-zero prior probability,p, is assigned toH0(0≤α1<p) and the remaining prior probability is spread over alternate values of θ that the probability thatH0will eventually be rejected when true is