Final answer:
The best guess for the number of heads in 1,000 flips of a fair coin is 500, based on the theoretical probability of 50% for each flip and the law of large numbers.
Step-by-step explanation:
If we flip a fair coin 1,000 times, the best guess for the number of times the coin would come up heads is 500. This is because a fair coin has a 50 percent chance of landing on heads on any given toss, which is a theoretical probability. When we conduct a large number of trials, such as 1,000 coin flips, the results should closely align with the expected probability, due to the law of large numbers as demonstrated by Karl Pearson's experiment.
In practice, the actual number may vary slightly, and we could get a few more or fewer heads than this amount. However, 500 is the most likely number of heads to be obtained, based on the theoretical probability. The more times we flip the coin, the closer we can expect to get to this 50 percent mark. This convergence to the expected probability is due to the law of large numbers, which states that as the number of trials increases, the experimental probability tends to get closer to the theoretical probability.