Tree Diagrams
- Visual tool that maps sequences of events or decisions into branching outcomes.
- Useful for computing and displaying probabilities for each path (e.g., die rolls, card draws).
- Applicable to decision analysis and game-theory strategy evaluation.
Definition
Section titled “Definition”Tree diagrams are a graphical representation of a sequence of events or decisions and their possible outcomes. They are commonly used in probability and statistics to illustrate the various possibilities and the corresponding probabilities of each event occurring.
Explanation
Section titled “Explanation”A tree diagram begins with an initial event or decision and branches outward to represent the possible subsequent outcomes or choices. Each branch corresponds to one possible outcome, and probabilities can be assigned to branches to show the likelihood of each path. Tree diagrams are used both to enumerate possibilities (for counting or probability) and to structure decision processes that include costs, benefits, or strategic interactions.
Examples
Section titled “Examples”Rolling a die
Section titled “Rolling a die”The tree diagram starts with the initial event of rolling the die, and then branches out to the possible outcomes of rolling a 1, 2, 3, 4, 5, or 6. For each of these outcomes, the probability would be 1/6 since there is an equal chance of rolling any number on a die.
Drawing a card from a deck
Section titled “Drawing a card from a deck”The tree diagram starts with the initial event of drawing a card, and then branches out to the four suits of cards: hearts, diamonds, clubs, and spades. For each of these suits, there are 13 possible cards that could be drawn (ace, 2, 3, etc. up to king). So the probability of drawing any specific card would be 1/52, since there are 52 cards in a deck.
Decision-making for business expansion
Section titled “Decision-making for business expansion”A tree diagram could be used to determine the most cost-effective option for a company to take in order to expand their business. The tree diagram would start with the initial decision of expanding the business, and then branch out to the different options available (such as opening a new location, increasing production, or acquiring a competitor). Each of these options would then branch out to the potential costs and benefits associated with them. The company can then use the tree diagram to weigh the pros and cons of each option and make an informed decision on the best course of action.
Rock–paper–scissors strategy (game theory)
Section titled “Rock–paper–scissors strategy (game theory)”A tree diagram could be used to determine the optimal strategy for a player in a game of rock-paper-scissors. The tree diagram would start with the initial decision of the player’s choice (rock, paper, or scissors), and then branch out to the possible outcomes based on the opponent’s choice. The player can then use the tree diagram to determine the probability of winning or losing based on their chosen strategy and the potential strategies of their opponent.
Use cases
Section titled “Use cases”- Probability
- Statistics
- Decision-making
- Game theory
Related terms
Section titled “Related terms”- Probability
- Statistics
- Decision-making
- Game theory