If there's a 30% chance it will rain over three days, what are the chances it rain any one of those days?

Question

Someone in my office said you do the opposite of the chance of it never raining, i.e. (.7)(.7)(.7) or 34.3, so you do 1 - 34.3 or 65.7% Yes/No?

Someone in my office said you do the opposite of the chance of it never raining, i.e. (.7)(.7)(.7) or 34.3, so you do 1 - 34.3 or 65.7% Yes/No?


To clarify question. There's is a 30% chance it will rain on Fri, 30% of rain on Sat, 30% on Sun. What are the chances it rains any one of those days?

Answer 1

Official smart-aleck answer:
There's a 100% chance it will rain. There's only a 30% chance it will rain on you.

Otherwise:
Using a binomial distribution considering there's a 30% chance it will rain on any of the three days:

The probability of it raining on 0 days is (1)(0.7)(0.7)(0.7) = 34.3%.
The probability of it raining on 1 day is (3)(0.3)(0.7)(0.7) = 44.1%.
The probability of it raining on 2 days is (3)(0.3)(0.3)(0.7) = 18.9%.
The probability of it raining on 3 days is (1)(0.3)(0.3)(0.3) = 2.7%.

Your officemates are correct in saying there's a 65.7% chance that it will rain at least once over the three-day period.

Answer 2

If you're referring to a meteorologist's report of "30% chance of rain during the next 3 days", then that is a continuous chance. Any portion of time within those 3 days, including the entire 3-day segment, will have exactly the 30% chance.

If instead you mean a mathematician's prediction that there is a 30% total chance of rain for a set number of periods within that 3-day span, then it depends entirely upon the length of the periods. Based upon your question, we can only guess that you are trying to divide the 3-day span into 3 * 1-day periods. If this is so, then you must invert the question such that you see there is a 70% chance that it will not rain at all during the entire span. Thus, there is an 88.9% chance that it will not rain on any given day (88.9% ^3 ~= 70.3%). So there is an 100% - 88.9% = 11.1% chance it will rain on any given day.

P.S. Your officemate's method could not be right, by simple reasoning. If each day had a whopping 65.7% chance of rain, then the chances of it raining at least once during the entire 3-day span would be *much* better than just 30%. ^.^

Answer 3

---If you're referring to a meteorologist's report of "30% chance of rain during the next 3 days", then that is a continuous chance. Any portion of time within those 3 days, including the entire 3-day segment, will have exactly the 30% chance---

The meteorologist report also includes spatial probability. So, the probability it rains in Baltimore may be slightly different than the probability it rains in Washington, DC.

The "30% chance within a three day period" probability is just that. You can't subdivide.

Answer 4

Like many other probability questions, weather probabilities remain the same for each occurrence. 30% chance of rain indicates a 30% chance for rain each of the three days. No day is any more of less likely to get rain, until the fronts move.

Answer 5

Stepping away from statistics here; when a weatherman says a 30% chance of rain, they are predicting it will rain 30% of the day. So if their prediction is correct, it will rain each day.

Answer 6

Its quite simple really, its 30% for each day untill it rains, then its a 0% chance.

Answer 7

10% for each day

Its all about odds and statistics:

(1/10)+(1/10)+(1/10)=(3/10)= 30%

I guess you'll have to look up how to deal with "either/or" events as opposed to "and" events

Answer 8

30% for each day.

Answer 9

About 33.3 Percent a day

Answer 10

DR is right. 30% for each day.

Interesting question (Y).