(Level 3) At the Large Hadron Collider they are hunting for the Higgs Boson. The engineers have developed a device that rings an alarm when a

Higgs Boson enters the device during a particle col- lision. However, the device isn't perfect. It will

work 80% of the time a Higgs Boson is released and enters the detector. Unfortunately, there is also a 2.1% chance the alarm will go off even when no Higgs Boson enters the device. If the alarm goes off, what is the chance that a Higgs Boson entered the detector? Note: use the assessment of physicists that there is a 50/50 chance that the Higgs Boson actually exits and if it exists, there is only a 10% chance it will enter the detector.