Determine whether the mother's preferences are consistent with her being an expected utility maximiser and explain

a) The mom has a chocolate bar that she can give to either Alice or Bill (her two children). She's indifferent between giving the chocolate to Alice or Bill, but she prefers the dad to choose randomly who to give it to rather than having to choose herself.

b) The mom has a chocolate bar that she can eat herself or give to either Alice or Bill. Her most preferred option is eating it herself. The second best option is the dad choosing randomly between giving it to her, Alice or Bill. The worst option is her having to choose between giving it to Alice or Bill.