Question

Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a 0.93 probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions. a. What is the probability that a single detection system will detect an attack? (to 2 decimals) b. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack? (to 4 decimals) c. If three systems are installed, what is the probability that at least one of the systems will detect the attack? (to 4 decimals) d. Would you recommend that multiple detection systems be used? - Select your answer -

Answer 1

luboni. pl detect) = 0.93 XnBinomial (m; 0.93) a) M=1 P(x) = () px qm-x P(x=1)= 1- P(x=0) 1- 620.9310.07 ° 0.93 0 2-o o.gg51 b) m = 2 P(x=)) = 1- P1x=0) = 1 - (30.93) 10.01) = 1o.gg51 c) m=3 P(x21) = 1 - Plx=0) - (3) 0.93j 10.07) = 0.9997 3-0 d) I yes, Multible detection system con be used because it increases probability yes