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Module 1: Introduction to probability

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Introduction to probability

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Introduction to probability

For many situations in our lives we are interested in the likelihood of
our success or not in the situation. We talk about whether the event is
likely or impossible. We might repeat the event several times or maybe many
hundreds of times. For each experiment we are interested in the final
chance or probability of getting the particular event. Sometimes we conduct
several experiments in which one event follows another, and we want to know
the chance of getting particular combination of results from the various
individual events.

To help us decide our next action in many situations in our lives, we
often collect data about previous cases of the situation. Then we need to
summarise the data collected so that we might sense of it. Some people like
to put all the results in tables to help them understand the trends and
range of the data. Many investigators draw graphs to summarise the data
that they have collected. In books and magazines everywhere you see
examples of bar and column graphs and pie charts and line graphs used by
the writer to emphasise important changes and trends in the data collected
in that situation.

A wide range of situations involve games of chance. These include card and
dice games; gambling with poker machines at the casino and horse racing;
and the forecasting of likely events based on car accident data and weather
reports. Often, in everyday life - for example, in horse racing or when
predicting outcomes or results - we use words like 'impossible, not likely,
possibly, and certain'. Gaining an understanding of these terms will help
us to understand probability.

Now, if we conduct probability experiments like throwing a die then we are
able to gather data about the various outcomes and the probability of
getting a particular result. For example, with a single throw of a die, we
might get a 6 then a 3, then 2 and then 6 again; and calculate that the
experimental probability of getting a 3 = 1/4 (one success from four
experiments). After many more throws it might be calculated that the
probability of getting a 3 equals a lower fraction closer to 1/5 or 1/6.
Theoretically, pr (3) = 1/6. Also, the topic of probability includes
calculations for finding the probability of getting any particular event in
a random situation and the alternative way of calculating the odds of
winning special events (odds for and odds against).

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