ITPEC FE Morning October 2018 Question 77

Topic: Corporate ActivitiesAlso asked in October 2023

When the weather tomorrow is sunny with 30% probability, cloudy with 50% probability, and rainy with 20% probability, which of the following strategies offers the highest expected value?

(Unit: Value)

Sunny	Cloudy	Rainy
Strategy S1	+80	+20	−40
Strategy S2	+60	+10	−10
Strategy S3	+40	+30	−20
Strategy S4	+50	+15	−15

a)S1b)S2c)S3d)S4

Explanation

S1, with an expected value of 26 — weight each outcome by its probability and add, then pick the largest sum.

Strategy	Sunny × 0.3	Cloudy × 0.5	Rainy × 0.2	Expected value
S1	24	10	−8	26
S2	18	5	−2	21
S3	12	15	−4	23
S4	15	7.5	−3	19.5

For example, S1: 80 × 0.3 + 20 × 0.5 + (−40) × 0.2 = 24 + 10 − 8 = 26.

Answer (a)

Why not others:

•(b) S2 — 21; it has the best worst case (−10), which is what a maximin choice would pick, not the highest expected value
•(c) S3 — 23; it has the best result for cloudy, the most likely weather, but a single likely outcome is not the expectation
•(d) S4 — 19.5, the lowest of the four

Key rule: Expected value = Σ(probability × outcome) over all states; choosing by the best worst case (maximin) or the most likely state answers a different question.

Corporate Activities · AI-written, may contain errors

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