How is probability defined in a mathematical context?

Probability in a mathematical context quantifies the likelihood of an event occurring and is expressed as a ratio. The correct definition articulates that probability is calculated by dividing the number of favorable outcomes (successful outcomes) by the total number of possible outcomes. This definition captures the essence of probability as it provides a clear, numerical representation of the likelihood of an event.

For instance, if you are rolling a six-sided die and want to calculate the probability of rolling a three, there is one favorable outcome (rolling a three) and six possible outcomes (1, 2, 3, 4, 5, and 6). Therefore, the probability would be 1/6.

This ratio approach not only establishes a clear formula for calculating probability but also provides insight into how likely an event is to occur within a specific set of circumstances.