The continuity axiom employed by von Neumann and Morgenstern holds that if $A>B>C$ then there exist some probabilities $p$ and $q$ such that $A p C>$ $B>A q C$. Let $$A=\$ 10,000,001$$ and $$B=\$ 10,000,000$$, and $C=50$ years in prison. (a) Do you think it is really true that there are any values of $p$ and $q$ such that $A p C>B>A q C$ truly describes your preferences? (b) Psychological studies suggest that most people cannot distinguish between very small probabilities, i.e. that their preferences over lotteries in which there is a small probability of a very bad outcome is unaffected by exactly how small the probability is. Does this show that there is something wrong with von Neumann and Morgenstern's theory?