Answered

Assume c and d function independently. for the system to function, either c or d must function.
a. if the probability that c fails is 0.08 and the probability that d fails is 0.12, find the probability that the system functions.
b. if both c and d have probability p of failing

Answer :

LammettHash
For the "system" to function, we require that [tex]C\cup D[/tex] occurs (i.e. the event that either [tex]C[/tex] or [tex]D[/tex] function properly). This occurs with probability

[tex]\mathbb P(C\cup D)=\mathbb P(C)+\mathbb P(D)-\mathbb P(C\cap D)[/tex]

but since [tex]C[/tex] and [tex]D[/tex] are independent,

[tex]\mathbb P(C\cup D)=\mathbb P(C)+\mathbb P(D)-\mathbb P(C)\mathbb P(D)[/tex]

We're given that [tex]\mathbb P(C^C)=0.08[/tex] and [tex]\mathbb P(D^C)=0.12[/tex], so

[tex]\mathbb P(C\cup D)=(1-0.08)+(1-0.12)-(1-0.08)(1-0.12)=0.9904[/tex]

If [tex]\mathbb P(C^C)=\mathbb P(D^C)=p[/tex], then

[tex]\mathbb P(C\cup D)=(1-p)+(1-p)-(1-p)^2=1-p^2[/tex]

Other Questions