QUESTION $14$

Prospect pair $1--$ choose between:

W: $(0\mathrm{.}2,$ $$4000)$

X: $(0\mathrm{.}25,$ $$3000)$

Prospect pair $2--$ choose between:

Y: $(0\mathrm{.}8,$ $$4,000)$

Z: $($$$3000)$

Part $($a$)$: What is the expected utility for Prospect pair $1($X$)?($Note: Please enter your answer rounded to the nearest whole dollar. For example, if your answer is $$1,234\mathrm{.}89,$ please input $1235$ in your answer box.$)(1$ mark$)$

Part $($b$)$: Based on the expected utility theory, which Options $($W or X$)$ would you choose for Prospect pair $1?($Note: If your answer is Option W$,$ you only need to input W in your answer box.$)(1$ mark$)$

Part $($c$)$: Ignoring the expected utility theory, would most people choose Options Y or Z from Prospect pair $2?($Note: You only need to input Y or Z in your answer box.$)(1$ mark$)$

Part $($d$)$: Please explain your rationale for your answer in Part $($c$)$ in less than $50$ words. $(2$ marks$)$