contestada

A system with 6 independent components is such that the system will fail if at least one of the individual components fail. the probability that a component fails is 0.02. let a be the event that the system fails. what is the probability of a ?

Respuesta :

LammettHash
The components operate independently, so the probability of "total" system failure is the same as the product of each probability of component failure. That is, if [tex]A_i[/tex] denotes the event that component [tex]i[/tex] fails, then

[tex]\mathbb P(A)=\mathbb P(A_1\cup\cdots\cup A_6)=\mathbb P(A_1)\times\cdots\times\mathbb P(A_6)[/tex]

The [tex]A_i[/tex] are independent and identically distributed, so [tex]\mathbb P(A_i)=\mathbb P(A_j)[/tex] for all [tex]i,j[/tex]. So

[tex]\mathbb P(A)=\mathbb P(A_1)^6=0.02^6=6.4\times10^{-11}=0.000000000064[/tex]

Otras preguntas