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

Given that P(B/A)=.97;   P(B/A')=.02;      P(A)=.1 Therefore, P(B'/A)=.03;   P(B'/A')=.98;     P(A')=.9 (1) P(missed)=P(B'nA)=P(B'/A)P(A) =(.03)(.1)=.003 (2)P(false alarm)=P(BnA')+P(AnB') =P(B/A')P(A')+P(B'/A)P(A) =(.02)(.9)+(.03)(.1)=.021 (3)P(A/B)=P(AnB)/P(B)=P(B/A)P(A)/P(B) Now P(B)=P(AnB)+P(A'nB)=P(B/A)P(A)+P(B/A')P(A')=(.97)(.1)+(.02)(.9)=.115 Hence P(A/B)=(.97)(.1)/.115=.843

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.