3.3.3 Decision Trees

• What is a decision tree used for in business?

  Aid decision-making
• Branches in a decision tree represent possible outcomes or alternatives
• Probabilities in a decision tree indicate the likelihood of specific outcomes.
• What are payoffs in a decision tree?

  Expected value or benefit
• The first step in using a decision tree is to identify the decision and possible alternatives
• Assigning probabilities to outcomes is a key step in using a decision tree.
• How do you choose the optimal decision in a decision tree?

  Highest expected value
• Match the node type with its description:

  Decision Node ↔️ Represents decisions to be made

  Chance Node ↔️ Represents uncertain events

  End Node ↔️ Represents final outcomes
• To use a decision tree, one must calculate the expected value
• What symbol is typically used to represent a decision node in a decision tree?

  Square
• The sum of probabilities at a chance node in a decision tree must equal 1.
• What should you identify for each chance node in a decision tree?

  Possible outcomes and probabilities
• The probabilities assigned to the branches of a chance node must sum to 1
• To calculate the expected value, you multiply the payoff by the probability of reaching that node.
• Steps to calculate the expected value in a decision tree:

  1️⃣ Multiply the payoff by the probability

  2️⃣ Sum the expected values for all paths

  3️⃣ Choose the decision with the highest expected value
• The expected monetary value (EMV) is calculated by summing the products of payoffs and probabilities for each path.
• Match the decision tree element with its description:

  Nodes ↔️ Represent decisions or chance events

  Branches ↔️ Represent possible outcomes or alternatives

  Probabilities ↔️ Indicate likelihood of outcomes

  Payoffs ↔️ Monetary value of final outcome
• Steps to use a decision tree:

  1️⃣ Identify the decision and alternatives

  2️⃣ Assign probabilities to outcomes

  3️⃣ Calculate expected value for each path

  4️⃣ Choose the path with the highest expected value
• What is represented by decision nodes in a decision tree?

  Decisions the maker must make
• What are the three key elements of a decision tree?

  Decision nodes, chance nodes, end nodes
• Decision nodes represent the decisions that the decision-maker must make
• Chance nodes in a decision tree are represented by circular nodes.
• Match the node type with its description:

  Decision Nodes ↔️ Square nodes representing decisions

  Chance Nodes ↔️ Circular nodes representing uncertain events

  End Nodes ↔️ Triangle nodes representing final outcomes
• What must the probabilities assigned to the branches of a chance node sum to?

  1
• Steps to calculate the Expected Monetary Value (EMV) in a decision tree:

  1️⃣ Identify the possible outcomes and probabilities for each chance node

  2️⃣ Multiply the payoff at each end node by its probability

  3️⃣ Sum the expected values for all possible paths

  4️⃣ Choose the decision with the highest EMV
• To calculate the EMV, you multiply the payoff by its probability
• What is the primary goal when calculating EMV in a decision tree?

  Maximize expected payoff
• A decision path with a higher EMV is always the optimal choice.
• Match the decision path with its EMV to identify the optimal choice:

  Path A ↔️ 65,000

  Path B ↔️ 72,000

  Path C ↔️ 60,000