1. Explain the three different approaches to probability theory in decision

making and give an example for each theory (6 marks)

The 3 different approaches to probability theory are intuition-based probability

or A Priori, relative frequency-based probability or empirical probability and

subjective probability.

In intuition based probability, depends on past experience or opinion of person.

An example is if arrival of cake ingredients would be delayed by 3 hours then

the baker would predict that the completion of the baking of the particular cake

would be delayed by 30% because this statement was based on past experience

dealing with similar delay in receiving the ingredients.

Equally likely assumed that each outcome of the experiment is equal so equal

probability is assigned to each outcome. If there are only 2 outcome then the

probability of the outcome would be 50%. An example can be seen in tossing a

coin where there are only 2 outcome that is either you will get the head or the tail.

Therefore the outcome of getting a tail is equal to getting a head and both equal

to 50%. Another example is when we roll a dice. We have 6 possible outcomes

and each are equally likely. And the outcome would be 1/6.

Relative Frequency Approach or Empirical Probability is ration of the number

of outcomes in which a specified event occurs to the number of trial in an actual

experiment. It estimates probabilities from experience and observation.

An example of relative frequency-based probability or empirical probability

can be seen in badminton fans predicting that there is 80-90% chance for Lin

Dan from China to beat Dato’ Lee Chong Wei of Malaysia based on their past

encounters. The formula that associated with this approach is:

probability = (frequency of the event occurrence divide by the total number of

observations)

Subjective probability is a probability derived from judgement of an individual’s

personal about whether a specific outcome is likely to occur. It does not cover

any formal calculations and only reflect the opinions and past experience of the

subject. It provides a quantitative way to express one’s belief and conviction

about each outcome. This probabilities differ from person to person because it is

subjective and it usually contains a high degree of personal bias. For example,

a child may thinks that his chance of getting an ‘A’ for the subject is 80%, his

teacher may think his change is 50% and the parents may think is 40%.