SOLUTION: a fire system has seven fail safe components. The probability of each failing is 0.07. Find these probabilities.
1. exactly 4 will fail
2.More then four will fail
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Question 1166409: a fire system has seven fail safe components. The probability of each failing is 0.07. Find these probabilities.
1. exactly 4 will fail
2.More then four will fail
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where the probability of success on any given trial is 
is given by:
\ =\ {{n}\choose{k}},(p)^k(1\,-\,p)^{n-k})
The probability of at most successes in trials where the probability of success on any given trial is is given by:
\ =\ \sum_{r=1}^k\,{{n}\choose{r}},(p)^r(1\,-\,p)^{n-r})
The probability of at least successes in trials where the probability of success on any given trial is is given by:
\ =\ \sum_{r=k}^n\,{{n}\choose{r}},(p)^r(1\,-\,p)^{n-r})
The probability of more than successes in trials where the probability of success on any given trial is is given by:
\ =\ \sum_{r=k+1}^n\,{{n}\choose{r}},(p)^r(1\,-\,p)^{n-r})
Make adjustments to the summation indices depending on exactly what you are looking for. Also note the following relationship that may save you some arithmetic:
\ =\ 1\ -\ P(\leq{k},n,p))
John
My calculator said it, I believe it, that settles it
I > Ø
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