Verified answer

Your question isn't really clear. Here's how I interpreted it:

A decider chooses between options d1 and d2. Then, one of three events (s1, s2, or s3) will happen, with the probabilities you mentioned. If the decider has chosen option d1, then she will lose $5000 in event s1, gain $1000 in event s2, and gain $10000 in event s3. If the decider has chosen option d2, then she will lose $15000 in event s1, lose $2000 in event s2, and gain $40000 in event s3.

Do I understand your question correctly?

Assuming yes...

Let's find the expected winnings from option d1. Multiply the payoffs (-5000, 1000, 10000) by their respective probabilities (.15, .5, .35) and add the results together:

Expected return = -750 + 500 + 3500 = 3250.

Now, let's find the expected winnings from option d2. Multiply the payoffs (-15000, -2000, 40000) by their respective probabilities (.15, .5, .35) and add the results together:

Expected return = -2250 - 1000 + 14000 = 10750.

In this case, option d2 has the higher expected payoff. It would seem the answer is B, but your question talks about expected losses, rather than expected winnings. Perhaps a closer reading of the problem would clarify.

I dont think the question is very clear, but I assume d1 and d2 are decision 1 and decision 2

d1=0.15*-5000 + 0.5*1000 + 0.35*10000

=3250

d2=0.15*-15000 + 0.5*-2000 + 0.35*40000

=10750 (B)