If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!

In article .com,
" wrote:
If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!

If it's a weather forecast, the probability is nil. ;-)


Cheers, Phred.

--
LID

The chance we will have rain in 48 hours is the chance that it will rain
today AND/OR the chance that it will rain tomorrow. This can be
translated in 1 - chance that it will stay dry today AND it will stay
dry tomorrow, thus

P_some_rain_in_48_Hours = 1 - P_dry_today*P_dry_tomorrow.

P_dry_today = 1-P_rain_today = 1-0.5 = 0.5
P_dry_tomorrow = 1-P_rain_tomorrow=1-0.4=0.6
P_dry_today*P_dry_tomorrow = 0.5*0.6 = 0.3

The chance that we will have some rain in the next 48 hours thus becomes
P_some_rain_in_48_Hours = 1 - 0.3 = 0.7

The probability of having rain on each day is simply the multiplication
of having rain today and having rain tomorrow, thus
P_rain_today_and_rain_tomorrow = 0.5 * 0.4 = 0.2

(Reality might be a little bit more complex, because the chance of rain
tomorrow might dependent on the fact that it rains today)

Willem


wrote:
If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!


--
Willem van Deursen, The Netherlands

replace _nospam@nospam_ for @ to get a valid email address
www.carthago.nl

Your last remark was one of the major points of our major points of
discussion, you said: "the chance of rain tomorrow might dependent on
the fact that it rains today."

Are these events, the forecast today and the forecast tomorrow
independent? Or, in fact, or they somehow related?

wrote in message
oups.com...
If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!


Before doing calculations we need to know what is meant by "50% chance of
rain today".
If a forecast for a region says 50% chance today it could mean that

1. It will rain over 50% of the region today
2. There is a 50% chance that any every point in the region will have rain
today
3. There is a 50% percent chance that it will rain somewhere in the region
today.

Interpretations 1 and 2 are almost (but not quite) mathematically
equivalent, but interpretation 3 is not.

I understand what you are saying, but regardless of the interpretation
of the forecast, why does the weatherman not tell us that we have a 70%
chance of rain over the weekend if there is a 50% chance on Saturday,
and a 40% chance on Sunday? It seems, if the standards rules of
probability apply to weather forecasts, that this would greatly enhance
weather reports, but since it is done I suspect there is a reason
beyond what my little mind can see. Or maybe it would just be
confusing to the general audience if they said the chance was 50% Sat,
40% Sun, and the accumulated percentage would be 70% for the weekend.
What's the answer?

On 23 Apr 2005 05:07:22 -0700,
, in
.com wrote:

+ Are these events, the forecast today and the forecast tomorrow
+ independent? Or, in fact, or they somehow related?

You're gonna hate this answer.

Depends. Sometimes they're tightly coupled, and sometimes not so
tightly coupled. Continuity says there is at least some degree of
relationship between day 1 and day 2.

James
--
Consulting Minister for Consultants, DNRC
I can please only one person per day. Today is not your day. Tomorrow
isn't looking good, either.
I am BOFH. Resistance is futile. Your network will be assimilated.

wrote:
If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!


If the forecast is 50% today and 40% tomorrow, then that's
what the forecast is. To then subject a forecast to some
statistical post-processing to obtain some less useful
homogenized number seems like a silly waste of time. This
exercise simply dilutes the original forecast with 24 hour
resolution to a less precise forecast with 48 hour
resolution. What's the purpose?

If you want to "better understand what our weather man is
really saying!" than don't attempt to combine consecutive
probabilistic forecasts into something the forecaster didn't
forecast.

Disclaimer: Opinions expressed are my own.

wrote:

If the weather forcast says we have a 50% chance of rain today, and a
40% chance of rain tomorrow, what is the chance that we will have rain
during that 48 hour period? And what is the probability that we will
have rain each day during that 48 hour period?

I've tried:

P(A||B) = A + B - A * B; # Is this approach right or wrong?

P(A&&B) = (A + B) / 2;

Please, help so that I may better understand what our weather man is
really saying!

Assuming those probabilities are accurate representations of the situation,
the probability rain occurs each day is simply (.5)(.4) = .2 = 20 %.

The probability it occurs at least one of those days depends (as people
mentioned) to what extent the events depend on each other. If it is a large
scale storm system expected to slowly pass the region, the events probably
depend on each other quite a bit - i.e., either the storm gets you both days
or neither. If these are expected to be from hit & miss showers because of
daytime convection, the events are probably to a large extent independent
(though the general flow regime and where showers occurred the previous day
has an influence on where they occur today).

If the events are independent, the probability rain occurs at least one
day is (as mentioned) 1 - the probability it occurs neither, which is:

1 - (.5)(1 - .4) = 1 - .3 = .7 = 70 %

So the best you can say for certain is that the probability P is :

50 % = P = 70 %

I.e., if they are completely dependent, it must be at least the value of that
for the highest day, and the highest it can be is if they are independent.

To what extent probabilities represent the actual situation is another issue.
They must be subjective to some extent. Even if you devise an algorithm
such as MOS to objectively correlate probability of rain with the conditions
expected, some subjective decisions must be made when devising the algorithm.

Note that the "probability of rain" as typically defined in forecasts does
not strictly mean whether rain occurs, but whether at least .01 inches is
measured. I.e., it is the probability of "measurable precipitation".

Joseph Bartlo wrote:

Assuming those probabilities are accurate representations of the situation,
the probability rain occurs each day is simply (.5)(.4) = .2 = 20 %.

That is also if the events are conisdered independent. If they were
completely dependent, it'd be

20 % = P = 40 %

I.e., the greatest it can be is that of the lowest day.