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I found a question posted here regarding a 5% chance of fire per month, and how does one take that probability out to one year:

Calculating probabilities over longer period of time

I follow the original explanation (see below). My question is why do you have to find the probability of no fire in the month (0.95) and then take that to the power of 12? Why can't you just do (0.05)^12?

Original Answer:

In all calculations, we will assume independence. That may not be reasonable in the case of forest fires.

Suppose that the probability of a fire in the course of a month is 0.05, that is, 5%, which is very high for any individual structure.

Then the probability of no fire in the month is 0.95.

The probability of no fire for 12 months in a row is then (0.95)^12.

It follows that the probability of at least one fire in a year is 1−(0.95)^12.

This is about 0.45964.

desertnaut
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Alex
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1 Answers1

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Calculating $0.05^{12}$ gives you the chance that you have a fire every month (assuming the events are independent-with that many fires I would question the assumption). It is a fine answer to a different question. You are being asked for the chance of at least one fire in a year. You could calculate the chance of $12$ fires (which you have done), and $11$ fires and $10...$ but that would be a lot of work. The approach you have at the end is to recognize that the chance of at least one fire is (1- the chance of no fires). If you want $12$ successive months of no fires, you must multiply the chances of no fire in each month.

Ross Millikan
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