Question

Recall Babitha's game: three options with probabilities 0.4, 0.5 and 0.8, giving likely gains of $100, $80 and $50 respectively (all three have the same expected value of $40, and Babitha, being risk taking, was shown to favour the first, most spread-out option when she can play repeatedly).

Continuing with the previous question, suppose Babitha can only play one more game. Which theory would help in arriving at a better decision?

• A. Expected Value
• B. Expected Utility
• C. Both theories will give the same result.
• D. Data is insufficient to answer the question.

Hint:

A single play gets no benefit from the law of large numbers, so expected value is useless here, but applying expected utility properly needs actual utility numbers, not just the qualitative fact that Babitha is risk taking.

Answer 1

The Correct Option is D

Step 1: Separate 'which theory is right in principle' from 'which theory can we compute.'
In principle, for a single, one-off gamble, expected utility (which encodes a person's actual risk attitude through the curvature of $u$) is the theoretically appropriate tool, while plain expected value is meant for repeated play, where the law of large numbers smooths outcomes out over many trials. Since Babitha now has only one game left, expected value has lost its main justification.

Step 2: Check expected value anyway.
$0.4 \times 100 = 40$, $0.5 \times 80 = 40$, $0.8 \times 50 = 40$; every option ties at $40, so even if we tried to use expected value here, it gives us zero information to prefer one option over another.

Step 3: Check whether expected utility is actually usable.
Applying expected utility for real requires plugging real numbers into $u(100)$, $u(80)$ and $u(50)$, meaning we would need to know Babitha's exact utility function, not just that it is convex. The passage and the earlier question give us only the label 'risk taking,' a qualitative description of the curve's shape, with no formula or numbers attached to it.

Step 4: Combine both findings.
Expected value theoretically no longer applies well to a one-shot decision, and even if we lean on the more appropriate expected utility theory, we lack the actual utility numbers needed to compute it. With neither route giving us a computable, defensible recommendation, the only honest conclusion is that we simply do not have enough data to say which theory leads to a better decision for Babitha's last game.

Final Answer:
Data is insufficient to answer the question. \[ \boxed{\text{Data insufficient}} \]