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# Three components are connected to form a system as shown in the accompanying diagram. Because the components in the $2-3$ subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the $2-3$ subsystem.The experiment consists of determining the condition of each component: $S$ (success) for afunctioning component and $F($ failure) for a nonfunctioning component.(a) What outcomes are contained in the event $A$ that exactly two out of the three components function?(b) What outcomes are contained in the event $B$ that at least two of the components function?(c) What outcomes are contained in the event $C$ that the system functions?(d) List outcomes in $C^{\prime}, A \cup C, A \cap C, B \cup C,$ and $B \cap C$ .

## (a) A ={SSF, SFS, FSS} $\\$(b) B ={SSS, SSF, SFS, SSS} $\\$(c) C ={SSS, SSF, SFS}$\\$(d) C0 ={SFF, FSS, FSF, FFS, FFF}A [ C ={SSS, SSF, SFS, FSS}A \ C ={SSF, SFS}B [ C ={SSS, SSF, SFS, FSS}B \ C ={SSS, SSF, SFS}

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Probability Topics

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Okay, So? Well, even a is exactly two out of the three component function. Okay? Which means say, one must be fell and I'll to my success. So we have these outcomes for the event, which is s f as have asked Have s okay. And for question beat You want us to determine you can be And we know your baby is alleys two of the component function Okay, which simply is just the even a plus the all success case which you have assets have plus s f s, F s and M plus trouble ass. Okay. And for question, See? Well you want us to determine event? See, an event, see, is their system functions. So we know in order to make the assistant function component, one must function. So therefore, component one must be asked. Okay, so therefore we'll have ah, all these outcomes for even see So you Messi should be go to, um us as a as I've asked and trouble ass. Okay, for next question while we know a b and C so see prime here It means it's not even see so we can at least all the alcohol except even see which are f ah s if, as f trouble f have ass s and s ff okay. And now that's trying to turn me any combination off even a any Bessie. So we will include all the all comes from human a any Bessie which are on S S f as f s of as s and trouble ass. An interception off, even a even see, she'll be equal to as as f and as address. And for the next one, we need to determine a combination of even Tiananmen. See, So we include only possible all kinds from even being Missy, which is he Go to s as, uh as f s uh, s trouble ass. So now let's determine the intersection off you NBN vincey, which is the common All comes from the both events, which should be equal to s as enough as fs and then to bless. And these are the answers for these questions.

Georgia State University

#### Topics

Probability Topics