PROBLEM ANALYSIS AND STATISTICS (8732)

TUTORIAL EXERCISES WEEK 8

Background for the usefulness of probability in the real world.

Introduction – Do critical thinkers need probability theory?

Out in the real world, trillions of events that depend upon random chance are occurring every second. A die is rolled, the gender of a child is determined, a plane crashes or an election is won. The word ‘probability’, refers to the likelihood of such events taking place.

More generally, probability theory provides us with tools for studying, measuring and summarising probabilities associated with random events.

Humans have a tendency to make definitive statements about uncertain future events. It is the task of the critical thinker to recognise such claims and investigate their validity.

Probability theory provides us with a framework that allows us to critically assess statements about random events.

How is probability theory used in Government?

Probabilistic methods are used across the full range of government administration areas including agriculture, defence, education, healthcare, environment, finance, infrastructure and welfare. For example, most governments use models to assess the probability of environmental risks such as flood, drought and earthquake. Further, most governments use probabilities extensively when choosing between projects – sometimes, the decision to pursue one project over another is based on statistical analyses of each project’s probable effect on the issue of interest.

How is probability theory used in Business?

Probability is used extensively throughout business to evaluate and quantify financial risk and opportunity. When decision makers are able to assess probabilities with greater precision, they are better positioned to minimise risk and maximise opportunity. In the following activity, we will see how probabilities can be used to maximise ad revenue for an internet blogger.

Applied example of statistics in the real world – Government health departments and disease clusters

Sometimes a greater than expected number of cases of a certain disease are found in a particular town or suburb. This can lead to community concern about the possible existence of a ‘disease cluster’. A disease cluster is the occurrence of a much greater than expected number of instances of a particular disease within a geographic region or period of time.

As diseases do not manifest evenly throughout communities or time, some regions will inevitably experience higher incidence rates for certain diseases, leading certain communities to speculate about the existence of a disease cluster. In most cases, the higher incidence is due to random variation and not an environmental factor. In a small number of cases however, real disease clusters do manifest and health departments must ascertain whether environmental factors are involved.

In Australia, health departments at the state level investigate possible disease clusters using probability models. Initially, the number of cases of the particular disease is compared with the expected number of cases. A probability is assigned to the likelihood of observing such a high incidence of the disease. If this probability is viewed to be unusually low, further investigation is pursued.

Question 1

Kathy is a blogger who has established two high traffic internet travel blogs. Kathy has recently become interested in the various ways in which her blogs can be monetised to provide extra income. One of the most popular ways of monetising internet blogs is ‘pay per click’ (PPC) online advertising. Pay per click is an internet advertising model that is used to direct traffic to other websites, where advertisers pay the hosting service (in this case, a blog) when the ad is clicked.

Kathy runs her domestic travel blog and international travel blog completely separately.

After shopping around, Kathy has found that a particular PPC provider will pay her 14 cents per ad clicked