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 0.89 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) 

          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 0.89 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)
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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 0.89 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)

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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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 0.87 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? 0.87 (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? 0.9657 (to 4 decimals) c. If three systems are installed, what is the probability that at least one of the systems will detect the attack? 0.9984 (to 4 decimals) d. Would you recommend that multiple detection systems be used? Yes

David N.
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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 0.91 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? 0.91 (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 -

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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 0.92 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 -

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Transcript

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00:01 So for this problem, to begin, we know that we're told to treat x as a binomial random variable, where n is some value, which is changing throughout the problem.
00:12 And the probability of success is 0 .89.
00:14 Also, we have the probability distribution function for a binomial given here.
00:18 N choose k times p to the power of k, times 1 minus p to the power of n minus k.
00:23 So for part a, the probability of an individual detection system detecting an attack, well, that probability is just given to us as 0 .89.
00:35 Then, for part b, we're looking for the probability that x is greater than or equal to 1.
00:42 Or we can think of that as 1 minus the probability that x equals 0.
00:49 Probability that x equals 0, that would be n -chus 0, which is just 1 times p to the power of 0, which is just 1, times 1 minus p, which is 0 .11, to the power of 2.
00:59 So, oh, pardon me, i need to be careful here, it's one minus all of that...
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