Final answer:
In coin toss experiments, the expected 50-50 split of heads and tails may not always occur in the short term, but over many repetitions, the results should approach the theoretical probability due to the law of large numbers. Variations in smaller samples are common, but larger sample sizes will typically yield results closer to the expected distribution.
Step-by-step explanation:
When flipping a coin, we often expect to get an equal number of heads and tails. However, in practice, the results may not align perfectly with these expectations because each flip is an independent event with a 50% chance of being heads or tails. It is more likely to observe fluctuations in smaller sample sizes, such as 10 coin flips. For instance, you might get seven heads and three tails instead of the expected five of each. When you and a partner combine your results from 10 tosses each, for a total of 20 tosses, the expectation is again an even number of heads and tails but the actual results may still deviate from the expected ten heads and ten tails.
If you compile results from an entire class, it amplifies the sample size which should, according to the law of large numbers, bring the relative frequency of heads closer to the theoretical probability of 0.5. For example, Karl Pearson's experiment tossing a coin 24,000 times produced results very close to a 50-50 split of heads and tails. Yet, short-term results can still differ significantly from the expected distribution; this is reflected in the relative frequency only aligning with the theoretical probability over many repeated trials.
In practical terms, if you toss 10 coins, the combined likelihood of getting the most common results, which are 6 heads and 4 tails, 5 heads and 5 tails, or 4 heads and 6 tails, is a substantial percentage of the time. However, the probability of getting an extreme result, such as all heads or all tails from 10 flips, is much lower. Such results are infrequent, and achieving one may take a considerable amount of time even if you perform flips frequently.