A project has two stages: Stage 1 yields $20,000 with probability 0.6; Stage 2 yields an additional $60,000 with probability 0.8 given Stage 1 success. If Stage 1 fails, Stage 2 is not attempted. What is the overall expected monetary value?

• A. $40,800
• B. $20,000
• C. $60,000
• D. $80,000

Answer: (A)

Think in terms of expected value across stages, weighting outcomes by their chances and recognizing that Stage 2 only happens if Stage 1 succeeds. If Stage 1 succeeds (probability 0.6), you receive 20,000 now, and Stage 2 can add 60,000 with probability 0.8, which gives an average extra of 0.8 × 60,000 = 48,000 when Stage 1 is successful. So the total expected payoff conditional on Stage 1’s success is 20,000 + 48,000 = 68,000. To get the overall expected value, multiply by the chance Stage 1 occurs: 0.6 × 68,000 = 40,800. Since Stage 2 doesn’t happen if Stage 1 fails, this correctly accounts for all paths.