Which of the following scenarios best illustrates the concept of expected utility?

Expected utility is a concept that is used to evaluate risky choices by considering the likelihood of various outcomes and the utility or satisfaction derived from those outcomes. In the context of the scenario given, a gambler calculating the chance of winning a bet based on odds is a direct application of this concept.

When a gambler assesses the odds of winning a bet, they are weighing the potential outcomes (winning or losing) along with the associated probabilities. The expected utility framework helps the gambler to determine whether the bet is worth taking by considering not just the amount of money that can be won (or lost) but also how much they value that potential outcome. This calculation of expected utility allows them to make a rational decision based on their preferences for risk and reward.

The other scenarios, while they involve decision-making, do not encapsulate the expected utility theory as clearly. Estimating happiness over careers or predicting grades based on study habits involves subjective evaluations of personal satisfaction or academic performance without the explicit calculation of probabilities and utilities. Similarly, planning a budget based on spending habits involves forecasting and financial planning but does not typically incorporate the broad notion of expected outcomes associated with uncertainty that is fundamental to expected utility.