Probability of precipitation

What do the probabilities of precipitation mean in weather forecasts? I
THINK that, say, 60% means the probability of 0.1 inch of precipitation
is 0.6.

If so, this leads to some fairly obvious contradictions. At
http://www.wunderground.com/cgi-bin/findweather/getForecast?query=seattle
right now the probability of precipitation on New Year's Day is 70%. But
clicking on the "Details" link for that day shows the day broken up into
4 6-hour periods, for all of which the probability is also 70%. See
http://www.wunderground.com/cgi-bin/findweather/getForecast?query=98101
&hourly=1&yday=1&weekday=Monday

Another example is Friday, Dec. 30. Probability for the day is 90%; the
details page for Friday shows it broken into 8 3-hour periods, for which
the probabilities are 70%, 70%, 90%, 90%, 90%, 90%, 80% and 80%,
respectively.

Now for the first example, the probability of less than 0.1 inch of rain
during the day would be 30% (1 - 70%). The same for each of the 4 6-hour
periods. And .3*.3*.3*.3 is 0.0089, the probablity of less than 0.1 inch
in all of the 4 periods together. Therefore the probablilty that at least
one of the 4 periods having more than 0.1 inch is 1 - 0.0089 = 0.991. And
yet the probability of precipitation for the whole day is supposed to be
only 70%.

For the second example the analagous probabilities are 0.9999 vs. 0.9.

Something seems to be wrong here. Am I correct?
.

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