Using the Expected Utility Theory answer the following question.

You are late for a party and are thinking about which store to visit on the way, to buy a drink to bring with you. Suppose:

Your utility for Guinness is 1.

Your utility for Natty Light is 0.

You prefer Guinness to Bud

You prefer Bud to Hoegaarden

You think a little more about the issue, since some stores may not have all these kinds of drinks, and find that:

You are indifferent between getting Bud for sure and a lottery that gives you Guinness with a probability of 0.9 and Natty Light with a probability of 0.1

You are indifferent between getting Bud for sure and a lottery that gives you Guinness with a probability of 0.6 and Hoegaarden with a probability of 0.4

Suppose all of your preferences satisfy the assumptions of expected utility theory. What is your utility for Hoegaarden?

(Please answer with a number rounded to three decimal places rather than with a fraction, e.g. 0.111 rather than 1/9).