a tree diafram
Empirical probabilities.
empirical probability is when you actually experiment with it and get data values, and theoretical probability is when you use math to make an educated guess.
When you have a model that describes the required situation well enough so that you can use scientific laws to calculate the probabilities of the outcomes of the experiment.
Repeated trials.
Sometimes it is possible to define a model for a trial or experiment and then use mathematical or scientific rules to determine the probability of the possible outcomes. Such a procedure gives theoretical probabilities.
If the events are independent then you can multiply the individual probabilities. But if they are not, you have to use conditional probabilities.
like for or we use + and for 'and' we use multiplication
A mixed strategy Nash equilibrium calculator can help you find the best strategies in a game theory scenario by calculating the optimal mix of strategies for each player. This tool considers the probabilities of each player choosing different strategies to find a balance where no player can improve their outcome by changing their strategy. By inputting the payoffs for each player's strategies, the calculator can determine the mixed strategy Nash equilibrium, which represents the most advantageous strategy mix for all players involved.
Players of card games often use strategies such as bluffing, reading their opponents' body language and patterns, keeping track of cards played, and making calculated decisions based on probabilities to outsmart their opponents and secure victory.
The process of elimination
Theoretical probability can be used to predict outcomes in real-world situations by applying the mathematical principles of likelihood based on known conditions. For instance, if you know that a die is fair, you can predict the probability of rolling a certain number (1 in 6). This approach is useful in various fields, such as finance for assessing risks, in sports for predicting outcomes of games, or in quality control for estimating the likelihood of defects in manufacturing. By understanding the underlying probabilities, decision-makers can make more informed choices and strategies.
To calculate the probabilities of compound events, you can use the multiplication rule or the addition rule, depending on whether the events are independent or mutually exclusive. The multiplication rule is used when the events are independent, and you multiply the probabilities of the individual events. The addition rule is used when the events are mutually exclusive, and you add the probabilities of the individual events.