Respuesta :
Answer: 0.997256
Step-by-step explanation:
Given : The probability that systems detects theft : [tex]p=\0.86[/tex]
Sample size : n= 3
Using Binomial probability formula :-
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
The probability that when a theft occurs, at least one of the 3 systems will detect it
=[tex]P(x\geq1)=1-P(x=0)[/tex]
[tex]1-^3C_0(0.86)^0(1-0.86)^3\\\\=1-(1)(1)(0.002744)\ [\becuase ^nC_0=1]\\\\=1-0.002744=0.997256[/tex]
Hence, the probability that when a theft occurs, at least oneof the 3 systems will detect it = 0.997256
Probability deals with the occurrence of a random event. The probability is 0.364 when the theft will occur in at least one of the three systems.
What is probability?
Probability means possibility. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank.
Each of the 3 systems detects theft with a probability of 0.86 independently of the others.
We know the formula
[tex]\rm P(x) = ^nC_x p^n(1-p)^{n-x}[/tex]
We have
p = 0.86
n = 3
Probability when the theft occurs, at least one of the 4 systems will detect it will be.
[tex]\rm P(x\geq 1) = 1-P(x=0)\\\\P(x\geq 1) = 1- ^3C_0 (0.86)^0 (1-0.86)^4\\\\P(x\geq 1) = 1 - (0.86)^3\\\\P(x\geq 1) = 0.364[/tex]
Thus, the probability when the theft occurs, at least one of the four systems will detect it is 0.364.
More about the probability link is given below.
https://brainly.com/question/795909
