Math Is Fun Forum

lizhikeng

Member

Registered: 2011-08-23

Posts: 2

A probablity problem

hi, I failed to solve the following problem , please help!
Suppose a electric power system with souce A, B and C, with capacities of Pa, Pb and Pc respectively. And a Load with demand of Pl. The three sources supply power to the load through three different routes, every route has it's own loss. The load can be supplied effectively only when the output of source(s) is greater than (Pl + loss of the coressponing routes).
Now we know the probability distribution of Pa, Pb, Pc, Pl and the losses, then how to express the probablity of "the Pl can be supplied effectively" ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: A probablity problem

hi lizhikeng

I'd work out what's the probability that none of the power supplies is sufficient and then subtract from 1.

Not sure what the engineers would do if more than one source can supply but that's not what you asked.

See diagram below.

Bob

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lizhikeng

Member

Registered: 2011-08-23

Posts: 2

Re: A probablity problem

hi lizhikeng

I'd work out what's the probability that none of the power supplies is sufficient and then subtract from 1.

Not sure what the engineers would do if more than one source can supply but that's not what you asked.

See diagram below.

Bob

Thanks for your reply. In this power system, the Load can be supplied by two or three sources simultaneously, that means even
Pa-La<PL and Pb-Lb<PL and Pc-Lc<PL, the Load can still be supplied effectively when Pa+Pb+Pc-(La+Lb+Lc) > PL or Pa+Pb-(La+Lb) > PL  or Pb+Pc-(Lb+Lc) > PL . For example, Let Pa=6,Pb=8 and Pc=10, La=2,Lb=4, and Lc=6, PL = 5, none of a sinlge source is sufficient, but the source combinations are ok, and by your expression, the probablity of "PL can be supplied" is 0