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 0.80 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

0.8 is the probability that a single detection system will detect a missile attack.

Step-by-step explanation:

We are given the following information:

We treat detection a missile attack as a success.

P(detecting a missile attack) = 80% = 0.8

Then the number of missile attack follows a binomial distribution, where

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 1

We have to evaluate:

0.8 is the probability that a single detection system will detect a missile attack.

(a) Probability that a single detection system will detect an attack is 0.80

Step-by-step explanation:

We are given that a reliability question is whether a detection system will be able to identify an attack and issue a warning. Assuming that a particular detection system has a 0.80 probability of detecting a missile attack.

The above situation can be represented through Binomial distribution;

where, n = number of trials(samples) taken = 1 detection system

            r = number of success

            p = probability of success which in our question is probability of

                   detecting a missile attack, i.e., 80%

LET X = a particular detection system

Also, it is given that a single detection system is taken,

So, it means X ~

Now, Probability that a single detection system will detect an attack is given by = P(X = 1)  

  P(X = 1) =

               = = 0.80 .

19

step-by-step explanation: