Hi,
It's been a while since I've had to do probability and I was hoping that someone could help me with a question. I have tried a lot of different questions that I have been able to do, but this one seems to be stumping me. For the system to work there has to be a path from A to B and/or from C to B. Each component fails independently with probability 0.06. Calculate the probability that it functions.
So P(system works) = P(A to B works) OR P(C to B works)
P(A to B works) = P(5 works) OR P(1 AND 2 works) OR P(1 AND 2 AND 3 works) OR P(1 AND 4 works)
= (1 - 0.06) + (1 - 0.06)^2 + (1 - 0.06)^3 + (1 - 0.06)^2
P(C to B works) = P(1 AND 5 works) OR P(2 works) OR P(2 AND 3 works) OR P(4 works)
= (1 - 0.06)^2 + (1 - 0.06) + (1 - 0.06)^2 + (1 - 0.06)^2
Do I need to be using the general addition rule in each step too? This is the bit that I'm confused about.
Thanks!
It's been a while since I've had to do probability and I was hoping that someone could help me with a question. I have tried a lot of different questions that I have been able to do, but this one seems to be stumping me. For the system to work there has to be a path from A to B and/or from C to B. Each component fails independently with probability 0.06. Calculate the probability that it functions.
So P(system works) = P(A to B works) OR P(C to B works)
P(A to B works) = P(5 works) OR P(1 AND 2 works) OR P(1 AND 2 AND 3 works) OR P(1 AND 4 works)
= (1 - 0.06) + (1 - 0.06)^2 + (1 - 0.06)^3 + (1 - 0.06)^2
P(C to B works) = P(1 AND 5 works) OR P(2 works) OR P(2 AND 3 works) OR P(4 works)
= (1 - 0.06)^2 + (1 - 0.06) + (1 - 0.06)^2 + (1 - 0.06)^2
Do I need to be using the general addition rule in each step too? This is the bit that I'm confused about.
Thanks!