How to Calculate Expected Value in Decision Tree?

Answer: To calculate expected value in a decision tree, multiply the outcome values by their respective probabilities and sum the results.

To calculate the expected value in a decision tree, follow these steps:

To calculate the expected value in a decision tree, follow these steps:

1. Identify Possible Outcomes:
   • Determine the possible outcomes associated with each decision or event in the decision tree.
2. Assign Probabilities:
   • Assign probabilities to each possible outcome based on their likelihood of occurrence. These probabilities can be estimated from historical data or domain knowledge.
3. Calculate Outcome Values:
   • For each possible outcome, determine its associated value or payoff. This value could represent monetary gains, utility, or any other relevant metric.
4. Compute Expected Value:
   • Multiply each outcome value by its probability and sum the results. The result is the expected value, which represents the average outcome considering all possible scenarios.
5. Example:
   • For instance, consider a decision tree representing investment decisions:
     • Outcome 1: Invest in Stock A (Probability: 0.6, Value: $500)
     • Outcome 2: Invest in Stock B (Probability: 0.4, Value: $700)
   • Expected Value = (0.6 * $500) + (0.4 * $700) = $300 + $280 = $580

Conclusion:

The expected value in a decision tree provides insight into the potential outcomes of different decisions, accounting for their probabilities. By calculating the expected value, decision-makers can make informed choices that maximize expected returns or outcomes.