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Joseph Bartlo · April 26th 05, 03:34 AM posted to sci.geo.meteorology

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".