Kaplan Question - Probability

hwiya320 · Posted: Mon Nov 24, 2008 4:22 pm Post subject: Kaplan Question - Probability

A machine is made up of two components, A and B. Each component either works or fails. The failure or non-failure of one component is independent of the failure or non-failure of the other component. The machine works if at least one of the components works. If the probability that each component works is 2/3 , what is the probability that the machine works?

a 1/9
b 4/9
c 1/2
d 2/3
e 8/9

Thanks!

Ossa · Posted: Mon Nov 24, 2008 6:07 pm Post subject: Re: Kaplan Question - Probability

Hi,

If the two components are A, and B, then the probabilty of the machine not working is the probability of both A and B failing which is (1-2/3)*(1-2/3)=1/9, and so the probability of the machine working is =1-probability of failure=8/9.