Final answer:
The correct method to determine the percentage chance for an event is to calculate the probability (option C). Probability involves dividing the number of ways an event can occur by the total number of possible outcomes. This is a mathematical method of quantifying the likelihood of outcomes in a systematic and theoretical approach.
Step-by-step explanation:
To determine the percentage chance that someone will or will not obtain a particular score, one would use the concept of probability. Likelihood deals with the chance of an event occurring and provides a way to quantify the likelihood of various outcomes. The question at hand is a mathematical problem related to the computation of chances, which makes options A (Pythagorean theorem), B (flipping a coin), and D (using algebraic equations) incorrect for calculating a precise percentage chance. The correct method to use is option C (By calculating the probability).
When calculating the probability of a particular event, and assuming all possible outcomes are equally likely, one can determine the theoretical probability. This calculation involves dividing the number of ways the event of interest can occur by the total number of possible outcomes. For example, if you flip a fair coin, the theoretical probability of getting heads is ½ or 50%, because there are two equally likely outcomes and one way to get heads.
Furthermore, to solve probability problems effectively, one would apply systematic approach methods such as the product rule and sum rule. The product rule is used when interested in the joint probability of two independent events occurring together, while the sum rule helps calculate the probability of one event or another occurring when the events are mutually exclusive.
Lastly, it's important to understand that probability is fundamentally about long-term expectations rather than predicting short-term results. This concept is exemplified by Karl Pearson's large coin toss experiment where the observed relative frequency of a large number of tosses was very close to the theoretical probability. This demonstrates the law of large numbers which states that as an experiment is repeated many times, the relative frequency of an event will tend to get closer to the theoretical probability.