In the original VNM theorem, lotteries are taken over global states of the world, meaning that preferences are expressed over mutually exclusive states of the world. Assuming there’s no other states of the world besides vanilla (V) and chocolate (C), your original lotteries are:

0.5*u(V) + 0.5u(c) = 1.5 + 4 = 5.4

against

1u(v) + 0u(c) = 3

so your preference goes to the first lottery. In the second set of lotteries you have

In the original VNM theorem, lotteries are taken over

globalstates of the world, meaning that preferences are expressed over mutually exclusive states of the world.Assuming there’s no other states of the world besides vanilla (V) and chocolate (C), your original lotteries are:

0.5*u(V) + 0.5u(c) = 1.5 + 4 = 5.4

against

1u(v) + 0u(c) = 3

so your preference goes to the first lottery. In the second set of lotteries you have

0.5*u(V) + 0.5u(c) = 3.5 + 6 = 9.4

against

1u(v) + 0u(c) = 7

You continue to prefer the first lottery.