Final answer:
The difference between Jess’s experimental probability of landing on 3 and the theoretical probability could be due to the low number of trials (25 spins) and potential bias in the spinner. The law of large numbers suggests that a larger sample size would likely yield an experimental probability that is closer to the theoretical probability.
Step-by-step explanation:
The difference between experimental and theoretical probabilities can be attributed to a concept called the law of large numbers, which states that as the number of trials in an experiment increases, the experimental probability tends to approach the theoretical probability. In the case of Jess spinning the pointer 25 times and obtaining a 16% experimental probability for landing on 3, as opposed to the theoretical probability of 25%, the discrepancy might be because 25 spins is not a sufficient number of trials for the experimental probability to align closely with the theoretical probability. Additionally, factors such as an unfair spinner or external influences could introduce bias, affecting the experimental probability.
Frequent fluctuations in results are expected in trials with a low number of repetitions, whereas with a large enough sample size, these fluctuations tend to even out. In the experiments mentioned with coin tosses, the results became closer to the theoretical probability when the number of flips was increased significantly. In gambling, for example, casino dice are designed to eliminate bias and ensure that each face is equally likely to occur, unlike everyday dice which might have slight weight differences due to carved spots.