So to summarize concisely (I apologize if my posts were a little wordy),
given the numbers:

The probability (P) of rain each day is 20 % = P = 40 %

and

The probability of rain at least one of the days is 50 % = P = 70 %

a range existing because it depends to what extent the events depend on
each other.

Actually, it could theoretically be as high as 90 % for rain during one of
the 2 days - if no rain the first day increased the probability of rain the
next.

Actually, the probability of rain in a forecast means that that percentage
of the forecast area will experience measurable precipitation, not that
there is that percentage chance that rain will fall on your head. This
might seem like hair splitting, but depending on the particular
microclimates of the forecast area the individual chance of experiencing
rain could range from 0 to 100%.

"Joseph Bartlo" wrote in message
...
Actually, it could theoretically be as high as 90 % for rain during one of
the 2 days - if no rain the first day increased the probability of rain
the
next.

William Oertell wrote:

Actually, the probability of rain in a forecast means that that percentage
of the forecast area will experience measurable precipitation, not that
there is that percentage chance that rain will fall on your head.

It can be, though there are many situations when an area (such as an NWS zone)
will either all get rain or none will. E.g., suppose a synoptic scale storm
system approaches. There are many possibilities depending on the track. Most
of those are that it will either pass close enough to cause rain over all or
nearly all of the zone or will miss. There is a MUCH smaller chance (among
the MANY possible tracks) of a glancing blow with would only cover part of the
zone with rain. In this case, the probability is not so much the percentage
of area that is expected to be covered, but the probability the storm hits the
zone or doesn't.

Your statement above applies very well to convective showers which are also
hit & miss but generally cover a much smaller area than the entire zone.
In that case, it may be very likely that some place in the zone will get
a shower, but they may only cover 30 % of it when all is done. Thus a 30%
chance for that situation.

For the former situation, I would say a 30 % chance is more so saying the
entire storm will probably miss the region, but there's a 30 % chance it
tracks favorably.

This might seem like hair splitting, but depending on the particular
microclimates of the forecast area the individual chance of experiencing
rain could range from 0 to 100%.

These microclimates are very difficult to determine. Some storms at my
location seem to defy any notion of microclimates. I.e., under very similar
conditions we sometimes get the convective showers and sometimes don't.
I think the probability is very useful in this case because it does seem
to some extent random.

Whatever the case for other forecasts, the probabilities forecast he

http://joseph-bartlo.net/mtpfor.htm

refer to whether .01 inches of precipitation is measured in my gauge
Then I can verify them.

I can say many things about how our microclimate affects temperatures, snow
accumulation and melting, etc. - but how it affects precipitation is very
difficult. Maybe that is because I know more about the former.