Suppose there is a covered bowl with 3 red balls and 6 other balls, which could be black or yellow. The Decision Maker [DM] doesn’t know how many black or yellow balls there are, other than there are 6 in total. The DM will choose one ball from the bowl; each ball is equally likely to be chosen. The DM is offered a choice between Option A, which pays off LKR1000 if a red ball is drawn (0 otherwise) or Option B, which pays off LKR1000 if a black ball is drawn (0 otherwise). The DM is then offered a choice between Option C, which pays off LKR1000 if a red or yellow ball is drawn (0 otherwise), or option D, which pays off LKR1000 if a black or yellow ball is drawn (0 otherwise). Find the expected utility basics of the theory of expected utility.

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Suppose there is a covered bowl with 3 red balls and 6 other balls,
which could be black or yellow. The Decision Maker [DM] doesn’t know
how many black or yellow balls there are, other than there are 6 in
total. The DM will choose one ball from the bowl; each ball is equally
likely to be chosen. The DM is offered a choice between Option A,
which pays off LKR1000 if a red ball is drawn (0 otherwise) or Option
B, which pays off LKR1000 if a black ball is drawn (0 otherwise). The
DM is then offered a choice between Option C, which pays off LKR1000
if a red or yellow ball is drawn (0 otherwise), or option D, which
pays off LKR1000 if a black or yellow ball is drawn (0 otherwise).

Find the expected utility basics of the theory of expected utility.

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