Expected Utility

Question

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)$50 \times 0.3 + 100 \times 0.2 + 150 \times (0.3 \times 0.2) = 44$

What happens the other $50%$ of the time? Are the two positive outcomes independent? — jlammy, Jan 05 '21 at 17:46
Yes, they are independent. We win nothing in all other cases. — Miles-can, Jan 05 '21 at 17:47

score 1 · Accepted Answer · answered Jan 05 '21 at 17:52

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.

Expected Utility

1 Answers1