Explain the independence axiom that underpins expected utility theory

Expected Utility Theory is a theory which estimates the likely utility of an action – when there is uncertainty about the outcome. It suggests the rational choice is to choose an action with the highest expected utility.It was first posited by Daniel Bernoulli who used it solve the St. Petersburg Paradox.
While analyzing uncertain situations, entities may or may not choose the action with the highest value of expected utility, depending on their risk aversion.
The expected utility theory finds application in public policy, as it explains that the social arrangement that maximizes the total welfare across society is the most socially right arrangement. The expected utility concept is also used to guide health policies. The expected utilities of various health interventions are used while framing health policies.

For example Letty finds a lottery ticket, that has a chance of $10 million and 50% chance of $0.A rich person offers to buy the ticket off him for $49,999,999 for sure.According to 'Expected Utility Theory' Letty should refuse the offer of rich person.

The independent axiom in such a theory would mean that the preference made by the decision maker in deciding between two outcomes is not affected by the mixing of the two possible outcomes. The probabilistic independent axiom extends this particular decision making to probabilistic decision making where the act of making decsions would vary with each predictions. Accordibg to probability axiom, the decsion making does not vary with the mixing of more pribability decisions that happens while choosing the outcome. Thus, we can see that independent axioms plays a good role in decision making and determina

tion of the manner of decision making in expected utilitites.