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Probability of something happening over a stated long period

If I have a Poisson distribution, X ~ Poisson(5) and this represents a spare part being used in a garage in a week, then the probability of more than 10 of this type of spare part being required in a week is fairly low : P(X > 10) = 0.0137

But over a longer period the likelihood that you will have a week where a quantity over 10 is required increases.

Eg over a year the probability of this happening are much greater than just in a one week period. How do you work out the probability of this happening? Is it 52 x 0.0137?

Is there any notation for this type of statement? Can someone explain if this is correct and how it works?
Original post by acomber
If I have a Poisson distribution, X ~ Poisson(5) and this represents a spare part being used in a garage in a week, then the probability of more than 10 of this type of spare part being required in a week is fairly low : P(X > 10) = 0.0137

But over a longer period the likelihood that you will have a week where a quantity over 10 is required increases.

Eg over a year the probability of this happening are much greater than just in a one week period. How do you work out the probability of this happening? Is it 52 x 0.0137?

Is there any notation for this type of statement? Can someone explain if this is correct and how it works?


By this reasoning what probability would you get for a 73 week period?

_____

You have an event (more than 10 parts are needed in a week) that either happens or it doesn't.

You have a probability that it happens.

You have 52 weeks where it might or might not happen.

_____

What's the probability that it happens at least one in the year?
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acomber
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Original post by BuryMathsTutor
By this reasoning what probability would you get for a 73 week period?

_____

You have an event (more than 10 parts are needed in a week) that either happens or it doesn't.

You have a probability that it happens.

You have 52 weeks where it might or might not happen.

_____

What's the probability that it happens at least one in the year?



in a 52 year period probability is 0.71. Over a 73 week period probability is one. ie probability is that it will happen once in a 73 week period. Is that what you are getting at?

You ask: What's the probability that it happens at least one in the year? The probability is 0.71??? that that event will happen.

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