What is a sample space diagram?

A sample space diagram is designed to show all possible outcomes of a probabilistic event in a clear and organized manner. This is critical in understanding the fundamentals of probability, as it allows one to visualize each potential outcome without omitting any. For instance, if you were to flip a coin, the sample space would include two outcomes: heads and tails.

This comprehensive listing is instrumental in calculating probabilities and making informed predictions about events. By clearly identifying every potential result, individuals can better analyze the likelihood of specific outcomes occurring.

The other options are more limited in scope. Showing only successful outcomes narrows the focus and does not provide the full picture needed for thorough probabilistic analysis. Representing probabilities using fractions may convey information about certain outcomes, but it does not entirely capture the array of all possible outcomes present in a sample space. Lastly, a diagram illustrating the dependence between events pertains to relationships between events rather than the total possible outcomes of a single event. Thus, the correct definition of a sample space diagram is one that encompasses all potential outcomes, demonstrating the foundation of probability theory.