Probability of Independent Events

Nature guards the precise details of the future, but mathematics gives us the master key to map the architecture of chance. We cannot declare exactly what will happen when we throw a pair of dice, but we can completely define the boundaries of what is possible. At its core, probability is a numerical measure representing the likelihood of a specific event occurring.

Traditional six-sided dice. While individual rolls are unpredictable, probability allows us to mathematically define the exact boundaries of their possible outcomes.
Traditional six-sided dice. While individual rolls are unpredictable, probability allows us to mathematically define the exact boundaries of their possible outcomes.

It is a discipline grounded in rigid limits. The probability of an event is always expressed as a real number between zero and one inclusive. These boundaries are absolute. A probability of zero indicates that an event is absolutely impossible. A probability of one indicates that an event is absolutely certain to occur. Between these two extremes lies the entire universe of risk, luck, and statistical mechanics.

To master the Praxis Core Mathematics exam, we must look closely at how these probabilities interact when multiple events occur in the same universe.