Math Problem Statement

Which option should be chosen based on the probabilities and payouts displayed in the decision-making task: Option A or Option B?

Solution

The image displays a decision-making task with two options: Option A and Option B, involving payout probabilities and amounts.

Key details:

  • Option A:

    • Payout amounts (R): R50, R80, R110, R140, R170, R200, R230, R260, R290.

    • Probabilities:

      • R50: 9%
      • R80: 30%
      • R110: 32%
      • R140: 19%
      • R170: 8%
      • R200: 2%
      • Higher values (R230-R290): 0%.
    • The description mentions:

      • A 9% chance to get R50 or less.
      • A 91% chance to get more than R50.
  • Option B:

    • Payout amounts (R): R50, R80, R110, R140, R170, R200, R230, R260, R290.

    • Probabilities:

      • R50: 35%
      • R80: 17%
      • R110: 12%
      • R140: 10%
      • R170: 8%
      • R200: 6%
      • R230: 5%
      • R260: 4%
      • R290: 3%.
    • The description mentions:

      • A 35% chance to get R50 or less.
      • A 65% chance to get more than R50.

Decision Context:

  • Option A offers a higher chance of payouts greater than R50, but with some payouts occurring at lower probabilities.
  • Option B has a higher chance (35%) of the smallest payout (R50), but smaller payouts are more evenly distributed across higher values compared to Option A.

Would you like further assistance with the decision analysis, risk calculation, or probabilities interpretation?

Related Questions:

  1. How do expected values of both options compare?
  2. What does the risk preference imply in choosing between these options?
  3. How could these probabilities be visually interpreted in a cumulative probability graph?
  4. What strategies could be applied in decision-making under risk for this task?
  5. How might this task relate to concepts in behavioral economics?

Tip:

Expected value calculation is a great tool to compare options, but incorporating your personal risk tolerance is crucial for making decisions.

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Math Problem Analysis

Mathematical Concepts

Probability
Expected Value
Risk Analysis

Formulas

Expected Value = Σ(Probability * Payout)
Risk Analysis involves comparing variance and probability distributions

Theorems

Law of Total Probability
Expected Value Theorem

Suitable Grade Level

College Level (Decision Theory, Behavioral Economics)