\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider a rare alien signal that is present in approximately 1 out of every 10,000 radio scans conducted by a space observatory. A signal detector has the following characteristics:
  • Sensitivity: If an alien signal is present, the detector correctly identifies it as positive 98\(\pourcent\) of the time.
  • Specificity: If no alien signal is present, the detector correctly identifies it as negative 96\(\pourcent\) of the time.
Find the probability in percent that an alien signal is actually present if the detector returns a positive result (round to 1 decimal place):
\(\PCond{\text{Signal}}{\text{Positive}} = \)
\(\pourcent\)