ITPEC FE Morning October 2018 Question 77
ITPEC FE Morning October 2018 — Question 77 of 80
Expected Value Calculation — Choose the strategy with the highest weighted payoff across all scenarios.
The expected value (EV) for each strategy is calculated as:
EV = P(Sunny) × Value(Sunny) + P(Cloudy) × Value(Cloudy) + P(Rainy) × Value(Rainy)
With probabilities: Sunny = 0.3, Cloudy = 0.5, Rainy = 0.2:
- •S1: 0.3 × 80 + 0.5 × 20 + 0.2 × (−40) = 24 + 10 − 8 = 26
- •S2: 0.3 × 60 + 0.5 × 10 + 0.2 × (−10) = 18 + 5 − 2 = 21
- •S3: 0.3 × 40 + 0.5 × 30 + 0.2 × (−20) = 12 + 15 − 4 = 23
- •S4: 0.3 × 50 + 0.5 × 15 + 0.2 × (−15) = 15 + 7.5 − 3 = 19.5
The correct answer is a) S1 with the highest expected value of 26.
Why not the others:
- S2 (21): Lower payoffs across all scenarios compared to S1
- S3 (23): Strong in Cloudy but weaker in Sunny, which pulls EV down
- S4 (19.5): Most balanced but lowest overall expected value
Key rule: Expected value = Σ (probability × outcome). Always multiply each outcome by its probability and sum them. The strategy with the highest sum is optimal under the expected value criterion.
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