Final answer:
The correct statement is that Tracie spins the spinner 1,000 times, it would land on red close to 250 times, assuming red has a theoretical probability of 0.25. This aligns with the law of large numbers stating that as the number of trials increases, the relative frequency approaches the theoretical probability.
Step-by-step explanation:
The question at hand deals with the concept of theoretical and relative frequency probabilities related to a spinner and the outcomes of spinning it multiple times. It touches on an important statistical principle known as the law of large numbers, which suggests that as the number of trials (or spins, in this case) increases, the relative frequency of a specific outcome (like landing on red) will get closer to the theoretical probability.
When we analyze the given statements one by one, it becomes apparent that the theoretical probability will not change with each spin - it is determined by the physical design of the spinner. However, the relative frequency of it landing on red will begin to stabilize around the theoretical probability given enough spins, as observed in Pearson's coin toss experiment. If the statement suggests that 'Tracie spins the spinner 1,000 times, it will land on red close to 250 times', it seems to align with the assumption that the spinner's segments are equally likely to be landed on (assuming 4 equal segments).
True Statement
Therefore, the true statement is: if Tracie spins the spinner 1,000 times, it would land on red close to 250 times. This is based on the assumption that red occupies 1/4th of the spinner space, giving it a theoretical probability of 0.25, or 25%. A large number of spins will likely yield results close to this probability under the law of large numbers.