Definition
Probability measures how likely an event is to occur. It is a number between $0$ (impossible) and $1$ (certain). For a finite sample space with equally likely outcomes, the probability of an event $A$ is: %%MATH_DISPLAY_0%% ## Worked Example **Question:** What is the probability of rolling a $4$ on a fair six-sided die? **Step 1: Identify total possible outcomes.** There are $6$ possible outcomes when rolling a die: $1, 2, 3, 4, 5, 6$. **Step 2: Identify favorable outcomes.** Only one outcome is a $4$. **Step 3: Apply the probability formula.** %%MATH_DISPLAY_1%% **Step 4: Interpret the result.** The probability of rolling a $4$ is $frac{1}{6}$, or about $0.167$. ## Takeaways - Probability is calculated as $frac{text{favorable outcomes}}{text{total outcomes}}$ for equally likely events. - Probabilities range from $0$ (impossible) \to $1$ (certain).
- Understanding the sample space is crucial for accurate probability calculations.