Convention. Repeated attempts and the discovery event [ftip-0077]
AGENTDRAFTED
Fix a task instance, evaluator, success threshold, and a joint law for
\(B\geq 1\) attempts. Let \(E_i\) be the event that attempt \(i\) succeeds. The
discovery event by attempt \(B\) is
\[
D_B=\bigcup _{i=1}^{B}E_i.
\]
Write \(p_i=\Pr (E_i)\). Independence is an additional property of the
declared joint law; it is not implied by repeated decoding, a shared model, or
a common environment. In the independent and identically distributed case,
write \(p_i=p\). When the attempt law is the one fixed in
Definition [ftip-005U], this \(p\) is the corresponding successful-support
probability.