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: Recall why expected value made sense before.
Expected value is only a reliable guide to decision making when a gamble is played over and over, because the law of large numbers guarantees that the realised long-run average will settle close to the theoretical expected value. That is why it was reasonable to lean on expected value logic when Babitha (or Babu, in the earlier question) could play many times.

Step 2: See what changes when only ONE game is left.
With just a single play, there is no averaging left to happen, the law of large numbers simply does not apply to one draw. So plain expected value (all three options tie at $40 here) cannot meaningfully guide a single, one-shot decision, and in principle expected utility, which is built to value a single risky outcome according to a person's own utility curve, is the theoretically correct tool for a one-shot choice.

Step 3: Check whether we can actually USE expected utility here.
To compute expected utility for real, we would need actual numeric values for \(u(100)\), \(u(80)\) and \(u(50)\), that is, we would need to know Babitha's precise utility function, not just its general shape. All we are told is the qualitative fact that Babitha is 'risk taking,' which tells us her utility function is convex in shape, but gives us no numbers to plug in.

Step 4: Conclude what this means for the answer.
Expected value cannot help because all three options tie and expected value ignores risk attitude entirely. Expected utility is the theoretically right tool for a one-shot decision, but we cannot actually compute it without knowing the exact utility function, only its shape. Since neither theory can be applied all the way through to a firm numeric recommendation with the information given, the honest answer is that the data given is not enough to say which theory would produce a better decision here.

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