Question 3. (20 marks) In this question we will consider two decision problems:

The Three-Colour Problem.

An urn contains 9 balls. Exactly three balls are Red. Each of the remaining six balls are either Yellow or Black. Consider the following:

Option a Win 100 if a red ball is drawn, zero otherwise

Option b Win 100 if a yellow ball is drawn, zero otherwise.

Most people strictly prefer option a over option b. Now consider the following options:

Option a' Win 100 if a red or a black ball is drawn, zero otherwise.

Option b' Win 100 if a yellow or a black ball is drawn, zero otherwise.

Most people strictly prefer option b' over option a' .

The Two-Colour Problem.

There are two identical urns, urn 1 and urn 2. Both urns contain 100 balls. Urn 1 contains 50 red balls and 50 blue balls. Urn 2 contains 100 balls, each of which is either red or blue. Consider the following:

Option c Win 100 if a red ball is drawn from urn 1, zero otherwise.

Option d Win 100 if a red ball is drawn from urn 2, zero otherwise.

Most people strictly prefer option c over option d. Now consider the following options:

Option c' Win 100 if a blue ball is drawn from urn 1, zero otherwise.

Option d' Win 100 if a blue ball is drawn from urn 2, zero otherwise.

Most people strictly prefer option c' over option d' .

Discuss the reasons why such preferences might be prevalent and discuss the implications for (subjective) expected utility theory and its underlying principles.