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, what is 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 systems will detect the attack? d. Would you recommend that multiple detection systems be used? Explain.

          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, what is 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 systems will detect the attack?
d. Would you recommend that multiple detection systems be used? Explain.

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Added by Brian P.

Essentials of Modern Business Statistics

David R. Anderson, Dennis J.… 5th Edition

Chapter 5

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Solved by Expert Evelyn Cunningham

08/20/2021

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The probability that a single detection system will detect an attack is given as 0.90 or 90%. b. If two detection systems are installed in the same area and operate independently, the probability that neither system detects the attack is (1-0.90) * (1-0.90) = Show more…

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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, what is 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 systems will detect the attack? d. Would you recommend that multiple detection systems be used? Explain.

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00:01 We are using binomial probability to solve this question.

00:11 And when you're doing binomial probability, the probability can be found by using ncx times p to the x times q to the n minus x, where p represents the probability of success and q represents the probability of failure.

00:36 And n is the number of trials.

00:46 So for part a, we want to determine the probability that a single detection system will detect an attack.

00:58 So therefore, n would be one.

01:01 And the probability of success, we're assuming that a particular detection system has a 0 .90 probability.

01:11 So our probability of success is going to be 0 .90.

01:17 So that means the probability of failure is going to be 0 .10.

01:22 So the answer to this, what is the probability that a single detection? well, that would be 0 .90.

01:31 For part b, we're best to look at a chart.

01:37 So this time n is going to be 2.

01:39 P is going to be 0 .90.

01:41 Q is going to be 0 .10.

01:44 So let's look at all our possible outcomes.

01:51 We might have neither of the two detect the attack.

01:56 We might have one of the two detect the attack, or we might have both detect the attack.

02:03 So we're going to substitute the 0, the 1, and the 2 in place of the x's in our formula.

02:11 So in your calculator, you're going to do 2cx times 0 .9 or 0 .90 to the x times 0 .10 to the 2 minus x, and x will change from 0 to 1 to 2.

02:30 And in doing so, you'll get a 0 .01, a 0 .18, and 0 .81 .1...

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