Answer:
The probability that at least one of the four systems will detect it is [tex]1-(0.01)^4[/tex].
Step-by-step explanation:
Consider the provided information.
Each of the four systems detects theft with a probability of 0.99 independently of the others.
Systems detects theft = p = 0.99
Systems fail to detects theft = q = 1-0.99=0.01
We need to find the probability that when a theft occurs, at least one of the four systems will detect it.
Pr (at least 1 systems detect theft) = 1 - Pr (none of the systems detect theft)
Pr (at least one systems detect theft = [tex]1-(0.01\times 0.01\times 0.01 \times 0.01)[/tex]
Pr (at least one systems detect theft = [tex]1-(0.01)^4[/tex]
Hence, the probability that at least one of the four systems will detect it is [tex]1-(0.01)^4[/tex].
