If an aircraft is present in a certain area, a radar correctlyregisters its pres

Question

If an aircraft is present in a certain area, a radar correctlyregisters its presence with probability .97. If it is notpresent, the radar falsely registers its presence with probability.02. We assume that aircraft is present with probability.1

Let A= {an aircraft is present}
Let B= {the radar registers an aircraft}

Find (1) the probability of missed detection,(2) probability offalse alarm, and (3) probability that an aircraft is present if itis registered

To me it seems as if the probability of missed detection, numberone, is .01. But I am confused with the given probability of.1 for when an aircraft is present. Always rate lifesaver,thanks!

Explanation / Answer

The probability that a missed detection occur is 0.03*0.1 sincethat will satisfy the aircraft being there but still not beingdetected. The probability that a false alarm occurs is 0.02*0.9 since thatwill satisfy the aircraft not being there and still falselyregistered. Now for the last one: The alarm can go off either if there is a false alarm or if thereis a corrctly registered event. So the chance that the larm will go off is 0.02*0.9 + 0.97*0.1 =0.115 wheras the chance that it has been correctly registered was0.97 so for every 115 times the alarm goes off, 97 of them have anaircraft present giving the probability = 97/115

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