Question

Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack. Answer the following questions using the binomial probability distribution:

1. what is the probability that one detection system will detect an attack?
2. 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?
3. If three systems are installed, what is the probability that at least one of the systems will detect the attack?
4. would you recommend that multiple detection systems be operated? Explain

Answer 1

Ans. Given P = 0.90 Formula binomial Probability : f(k) - ().pk (1-P)** a) n. 1 0.9 46. ().90' (1-0.90,11 b) na 0.18 = 0.81 f() = (* ). 90'.(9-6.90394 $(3) - ().0.90% (-0.90) ? Add the corresponding probabilities: P10131) - FO) + f(3) = 0.16 +0.81 - 0.99 n=3 0.027 : 0.243 0.729 f(): (?).6.901. (1-0.90)94 +(2). C). 0.90 (1-0-3503513 $(3) - C): 0.009 (1-0.999? Add the corresponding probabilities: Plazı) = f( + F(-) + f(3) = 0-037 +0.243 + 0.729 : 0.999 d) It is recommendable that multiple delection systems are used because three systems are used, then it is nearly impossible to not detect the attack.

a) 0.9

b) 0.99

c) 0.999

d) Yes