I am confused by something regarding expected utility calculation.
When we are calculating the expected utility where 2 positive outcomes can happen at the same time such as the example below:
We win 50 with probability of 0.3
We win 100 with probability of 0.2
How do we calculate the expected utility? Which of the options below is correct?
(1)$50 \times 0.3 + 100 \times 0.2 = 35$
(2)$50 \times 0.3 + 100 \times 0.2 + 150 \times (0.3 \times 0.2) = 44$
Because the two events are independent of each other, simply consider their outcomes one at a time. The expected utility of the first event is $50 \cdot 0.3 = 15$ while the expected utility of the second event is $100 \cdot 0.2 = 20$. Thus, the total expected utility is $15+20=35$. In other words, the first equation you listed is correct.