(10 points) An air defense system consists of n independent radar sets over a gi
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Question
(10 points) An air defense system consists of n independent radar sets over a given area. Assume each radar has a probability of 0.9 of detecting an airplane. The system declares an airplane is present if one or more of the radar detects an airplane. Find the probability the system will declare an airplane if (a) n 2, (b) n-4. (Hint: Let X-number of radar sets out of n that detects an airplane. What is the distribution of X?) (c) How large must n be in order for the system to declare an airplane with a 0.999 probability? 1.Explanation / Answer
Pr(Detects a airplane) = 0.9
(a) if n = 2 then it can be said the distribution ca be binomial.
so Pr(one or more radar will detect an airplane) = 1 - Pr(no radar will detect the airplane) = 1 - 2C0 (0.9)0(0.1)2 = 1 - 0.01 = 0.99
n= 4
Pr(one or more radar will detect an airplane) = 1 - Pr(no radar will detect the airplane) = 1 - 4C0 (0.9)0(0.1)4 = 1 - 0.0001 = 0.9999
(c) So, now here the detection probability is 0.999
Pr(one or more radar out of n will detect an airplane) = 1- Pr(no radar will detect the airplane) = 1 - nC0 (0.9)0(0.1)n = 1 - 0.1n = 0.999
0.1n = 0.001
n = 3
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