### Artificial IntelligenceAIMA Exercises

Tickets to a lottery cost 1. There are two possible prizes: a 10 payoff with probability 1/50, and a 1,000,000 payoff with probability 1/2,000,000. What is the expected monetary value of a lottery ticket? When (if ever) is it rational to buy a ticket? Be precise—show an equation involving utilities. You may assume current wealth of $k$ and that $U(S_k)=0$. You may also assume that $U(S_{k+{10}}) = {10}\times U(S_{k+1})$, but you may not make any assumptions about $U(S_{k+1,{000},{000}})$. Sociological studies show that people with lower income buy a disproportionate number of lottery tickets. Do you think this is because they are worse decision makers or because they have a different utility function? Consider the value of contemplating the possibility of winning the lottery versus the value of contemplating becoming an action hero while watching an adventure movie.

Tickets to a lottery cost 1. There are two possible prizes: a 10 payoff with probability 1/50, and a 1,000,000 payoff with probability 1/2,000,000. What is the expected monetary value of a lottery ticket? When (if ever) is it rational to buy a ticket? Be precise—show an equation involving utilities. You may assume current wealth of $k$ and that $U(S_k)=0$. You may also assume that $U(S_{k+{10}}) = {10}\times U(S_{k+1})$, but you may not make any assumptions about $U(S_{k+1,{000},{000}})$. Sociological studies show that people with lower income buy a disproportionate number of lottery tickets. Do you think this is because they are worse decision makers or because they have a different utility function? Consider the value of contemplating the possibility of winning the lottery versus the value of contemplating becoming an action hero while watching an adventure movie.

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