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Probability that none of machine's components fail
By Harnake Gill (P759) on Wednesday, March 17, 1999 - 11:04 am:

A piece of hospital equipment will function only if 3 components A,B and C are all working. The probability of A failing during one year is 0.05, that of B failing is 0.15 and that of C is 0.10. What is the probability of the equipment fails before the end of the year?

By Ben Parker (Bmp22) on Wednesday, March 17, 1999 - 11:21 am:

Hi there Harnake,

I'd tend to think of it like this:

For the machine to work, it means that all 3 components must work.

You can then work out the probability that the machine fails- because either it works or it fails and the basic rules of probability mean that

P(Machine works) + P(Machine fails) = 1

where P(X) means the probability that X happens.

So, work out the probability that each item works on its own- so P( A works) = 0.95, etc.

Now, using the fact that the events are independent (which I'm assuming from the way the question's worded), you can work out
P(Machine works), and get the answer from there.

Ask again if you don't know what it means for events to be independent.

Note that it's well worth being very comfortable with questions like these, as they tend to turn up all over GCSE and A-level, and once you've got the basic idea they're very easy.

Hope this helps,

Ben

By Harnake Gill (P759) on Wednesday, March 17, 1999 - 11:24 am:

Cheers Ben