# Thread: Calculating Probabilities

1. ## Calculating Probabilities

If a mechanical fault in a car occurs once in every 120 days, and I drive the car 260 days per year, what is the probability of a mechanical fault occurring over that 260 day period. I thought that 260/120 is 2.167 days affected and then divide by 260 giving me a probability of 0.83%
I don't think I am doing this correctly, can anyone help
regards Robert

2. ## Re: Calculating Probabilities

hi,
I think the use of the Poisson distribution is approprkate with k=1 and the intensity lambda= 260/120.
regards

3. ## Re: Calculating Probabilities

Hi,
thanks very much. Can you explain what "k" is? & I am ok with lambda rate..

4. ## Re: Calculating Probabilities

hi,
the number of occurences, you calculate the probability of.
regards

5. ## Re: Calculating Probabilities

Not sure if this is an exercise or a real problem. From the way it's worded, Poisson sounds like overkill. On any given day the probability you WON'T have an accident is 119/120. You can figure out the probability you won't have a mechanical fault in any of the 260 days (ie, 119/120 to the power 260), then subtract that from 1.

Note that 260/120 is the expected number of faults. 0.00833 is the expected number per day. Neither answers the question posed. The trick to these is that you need the probability of at least one fault in 260 days, but you could have 1, 2, 3, 4,... or 260 (rare!) So simple proportion and ratio methods don't work.

6. ## Re: Calculating Probabilities

I'm assuming you would count 2 or 3 faults as "a fault occuring". I think rogojel's method is the probability of exactly 1 fault. You can also calculate that from the binomial theorem.

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