Military radar and missile detection systems are designed to warn a country of a
ID: 3060151 • Letter: M
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 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 -YesNoItem 4
Explanation / Answer
Since you have not mentioned in the question the exact probability of a single detector system to detect a missile attack, I just assume it is 'p'. My every answer will be in the form of p. If you have the value of p, then put it and get the answer.
a.) It will be p itself.
b.) P(no one of them detecting the attack) = (1-p)(1-p)
Thus, P(at least one of them detecting) = 1- (1-p)(1-p)
second method of solving this problem,
Let X be the number of detector which detected the missile attack, then X can be 0, 1 or 2
Now, P(X=1) = 2C1 * (p) * (1-p)
P(X=2) = 2C2* p*p
P(at least one of them would be) = P(X=1) + P(X=2)
c.) P(No one detecting the missile attack) = (1-p)(1-p)(1-p)
P( at least one detecting) = 1-(1-p)(1-p)(1-p)
d.) It depends on the value of P, If P value is bigger then we may chose but standard deviation of the multiple detection system then will also be high thus their chances of not being around the expected outcome increases.
So, it really comes down to the cost you want to pay agains the benefit you are getting by installing multiple detection system,