Respuesta :
Answer:
(a) 0.90
(b) 0.99
(c) 0.999
(d) Yes
Step-by-step explanation:
A particular detection system has a 0.90 probability of detecting a missile attack.
Let X = number of detection system that detects a missile attack.
The random variable X follows a Binomial distribution with probability of success as, p = 0.90.
(a)
Compute the probability that a single detection system will detect an attack as follows:
[tex]P(X=1)={1\choose 1}(0.90)^{1}(1-0.90)^{1-1}\\=1\times 0.90\times 1\\=0.90[/tex]
(b)
Compute the probability that at least one of the two systems will detect the attack as follows:
[tex]P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1-{2\choose 0}(0.90)^{0}(1-0.90)^{2-0}\\=1-0.01\\=0.99[/tex]
(c)
Compute the probability that at least one of the three systems will detect the attack as follows:
[tex]P(X\geq 1)=1-P(X<1)\\=1-P(X=0)\\=1-{3\choose 0}(0.90)^{0}(1-0.90)^{3-0}\\=1-0.001\\=0.999[/tex]
(d)
On using only one system the probability that a single detection system will detect an attack is 0.90.
On using two systems the probability that at least one of the two systems detecting the attack is 0.99.
And on using three systems the probability that at least one of the three systems detecting the attack is 0.999.
So as the number of system is increasing the probability of detecting the attack is getting closer to 1.
Thus, it would be wise to recommend that multiple detection systems be used.
