The two hypotheses (causes) which could condition the event (effect)
(=``trigger fired'') are ``'' and ``''. They are incompatible
(clearly) and exhaustive (90% + 10% = 100%). Then:
The S/N ratio is
. It is interesting
to rewrite the general expression of the S/N ratio
if the effect is observed as
This formula explicitly shows that when there are
, the experiment must be very selective,
, in order to have a decent ratio.
(How does change if the particle has to be identified by
two independent detectors in order to give the trigger?
Try it yourself, the answer is .)