ITPEC FE Morning October 2023 Question 77
ITPEC FE Morning October 2023 — Question 77 of 80
Calculate E = Σ(probability × outcome) for each strategy:
| Strategy | Sunny (0.3) | Cloudy (0.5) | Rainy (0.2) | Expected Value |
|---|---|---|---|---|
| S1 | 0.3×80=24 | 0.5×20=10 | 0.2×(−40)=−8 | 26 |
| S2 | 0.3×60=18 | 0.5×10=5 | 0.2×(−10)=−2 | 21 |
| S3 | 0.3×40=12 | 0.5×30=15 | 0.2×(−20)=−4 | 23 |
| S4 | 0.3×50=15 | 0.5×15=7.5 | 0.2×(−15)=−3 | 19.5 |
S1 yields the highest expected value of 26.
Why not others:
- (b) S2 — E=21, lower than S1 despite smaller losses; the gain difference outweighs risk reduction
- (c) S3 — E=23, competitive but S1's sunny upside (+80) overcomes the rainy penalty
- (d) S4 — E=19.5, worst overall; moderate gains in all scenarios don't compensate
Key rule: Expected value = Σ(probability × outcome); always multiply each outcome by its weight before summing.
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