B-1 is wrong because you’re not using marginal utility. On the second repetition, U(marginal)[$1,000,000] is either 1 or 0.1 depending on whether you lost or won on the first play. You can still add the utilities of events up, but the first and second plays are different events, utility-wise, so you can’t multiply by 2. The correct expression is:
(50%U($0) + 50%U(the first million)) + (50%U($0) + 50%(50%U(the first million) + 50%U(the second million)))
B-1 is wrong because you’re not using marginal utility. On the second repetition, U(marginal)[$1,000,000] is either 1 or 0.1 depending on whether you lost or won on the first play. You can still add the utilities of events up, but the first and second plays are different events, utility-wise, so you can’t multiply by 2. The correct expression is:
(50%U($0) + 50%U(the first million)) + (50%U($0) + 50%(50%U(the first million) + 50%U(the second million)))
which comes out to .775.