 There are, of course, more complex cases of likelihoods involving statistical hypotheses. Consider, for example, the hypothesis that plutonium 233 nuclei have a half-life of 20 minutes—i.e., that the propensity (or objective chance) for a Pu-233 nucleus to decay within a 20 minute period is 1/2. The full statistical model for the lifetime of such a system says that the propensity (or objective chance) for that system to remain intact (i.e., to not decay) within any time period x is governed by the formula \(1/2^{x/\tau}\), where \(\tau\) is the half-life of such a system. Let \(h\) be a hypothesis that says that this statistical model applies to Pu-233 nuclei with \(\tau = 20\) minutes; let \(c\) say that some specific Pu-233 nucleus is intact within a decay detector (of some specific kind) at an initial time \(t_0\); let \(e\) say that no decay of this same Pu-233 nucleus is detected by the later time \(t\); and let \(b\) say that the detector is completely accurate (it always registers a real decay, and it never registers false-positive detections).  Then, the associated likelihood of \(e\) given \(h\) and \(c\) is this: \(P[e \pmid h\cdot b\cdot c] = 1/2^{(t - t_0)/\tau}\), where the value of \(\tau\) is 20 minutes.