\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In a futuristic society, 1 out of every 500 devices contains a rare quantum crystal as its power source. A crystal detector has been invented with the following properties:
  • Sensitivity: If a device has a quantum crystal, the detector correctly registers it as active 90\(\pourcent\) of the time.
  • Specificity: If a device does not have a quantum crystal, the detector correctly registers it as inactive 97\(\pourcent\) of the time.
Find the probability in percent that a device actually has a quantum crystal if the detector registers it as active (round to 1 decimal place):
\(\PCond{\text{Crystal}}{\text{Active}} = \)
\(\pourcent\)