Final answer:
The probability of landing on 2 out of 12 sections on a spinning wheel remains constant with each spin. Over a large number of spins, the relative frequency of landing on these sections will approach their theoretical probability, exemplifying the law of large numbers.
Step-by-step explanation:
The probability of landing on 2 out of 12 sections of a spinning wheel does not change the more you spin it, assuming the wheel is fair and balanced. Each spin is an independent event, meaning the outcome of one spin does not influence the outcomes of subsequent spins. According to the law of large numbers, the long-term relative frequency of landing on these sections will approach their theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes. This concept underlines that while individual experiments can yield varying results, as the number of repetitions increases, the observed probability becomes closer to the theoretical probability.
For example, if a fair coin is tossed many times, the relative frequency of heads will get closer to 50 percent, the theoretical probability. Similarly, with a fair die, the chance of rolling a number at least five (event E) is 2 out of 6, or approximately 33.33 percent. If you roll the die many times, the percentage of rolls resulting in a five or a six gets closer to this theoretical probability.