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 .90 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?b. If two detection systems are installed in the same area and operate independently, whatis the probability that at least one of the systems will detect the attack?c. If three systems are installed, what is the probability that at least one of the systemswill detect the attack?d. Would you recommend that multiple detection systems be used? Explain.

Answer 1

Answer:

A) 0.9

B) 0.99

C) 0.999

D) Yes, i will recommend.

Step-by-step explanation:

We are given that p = 0.9

Now, the formula for the binomial probability is given as;

f(k) = (n,k) (p^(k)) [(1-p)^(n-k)]

Thus;

A) n = 1;

f(1) = (1,1) (0.9)¹ [(1-0.9)^(1-1)]

= 1 x 0.9 x 1 = 0.9

B) n=2;

f(1) = (2,1) (0.9)¹ [(1-0.9)^(2-1)] = 2 x 0.9 x 0.1¹ = 0.18

f(2) = (2,2) (0.9)² [(1-0.9)^(2-2)] = 0.81 x 1 = 0.81

Thus;

P(X ≥ 1) = f(1) + f(2) = 0.81 + 0.18 = 0.99

C) n = 3;

f(1) = (3,1) (0.9)¹ [(1-0.9)^(3-1)] = 3 x 0.9 x 0.1² = 0.027

f(2) = (3,2) (0.9)² [(1-0.9)^(3-2)] = 3 x 0.81 x 0.1 = 0.243

f(3) = (3,3) (0.9)³ [(1-0.9)^(3-3)] = 0.729 x 1 = 0.729

P(X ≥ 1) = f(1) + f(2) + f(3) = 0.027 + 0.243 + 0.729 = 0.999

D) Yes, i will recommend that multiple detection systems are used, because when three systems are used, then it is nearly impossible to not detect the attack.