Probability theory is a branch of mathematics that deals with analyzing random events and quantifying uncertainty. It provides tools to calculate the likelihood of different outcomes, often expressed as numbers between 0 and 1.

🔹 Key Concepts:

1. Experiment: A process that produces outcomes (e.g., tossing a coin).

2. Sample Space (S): The set of all possible outcomes (e.g., for a coin toss: {Heads, Tails}).

3. Event (E): A subset of the sample space (e.g., getting a Head).

4. Probability of an Event (P(E)):

   $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

🔹 Example:

• If a die is rolled, the sample space is {1, 2, 3, 4, 5, 6}.

• The probability of rolling a 4 is:

  $$P(4) = \frac{1}{6}$$

🔹 Applications:

Used in statistics, finance, AI, risk assessment, game theory, and more.

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