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3.1 The Idea of Probability
In this section, we‟ll address what probability is (and isn‟t).
Example 1: A weather report by the National Weather Service (NWS) stated on July 31, 2011
that, overnight, there was a 50% chance of precipitation in the 85225 zip code in which
Chandler-Gilbert Community College is located. What does this mean
(SOURCE: www.crh.noaa.gov/)
SOLUTION: This is actually quite a loaded statement. One might want to say that, out of 100
times, it will rain 50 times. This is a very misleading approach for a couple of different reasons.
First off, what is meant by “times” We are only concerned with one time: overnight on July 31,
2011.
A probability is actually a measure of how likely something is to occur in the long-run. That is,
if something were to be repeated in trials over and over again then, theoretically, the specified
outcome would occur a certain percentage of time. Importantly, it must be noted that the
conditions under which we are measuring a probability must be in place in order for the
probability to be a valid measure.
In our case, NWS states that, under the exact same environmental conditions taking place
throughout the night of July 31, 2011, it would be expected to rain 50% of the time.
The graph below shows a hypothetical scenario in which there is a 50% chance of precipitation
under the set of conditions that occurred on the above night. Notice that it rained on the initial
day and so immediately the proportion (or probability) of rainy days is 100%. As the same
conditions occur on different days, sometimes it rains and sometimes it does not. Having noted
that, any given day has a 50% chance of precipitation. We notice that the proportion is quite
unstable at first, jumping from 100%, down to nearly 40%; However, as many days with this
same set of conditions pass (in the long-run), we notice that the proportion becomes more stable
and approaches the theoretical probability of 50%.
Statistics for Decision-Making in Business © Milos Podmanik Page 82