The probability of the next coin flip resulting in tails is always 0.5, or 50%, regardless of the past results of flipping the coin 100 times. This is because coin tosses are independent events and the probability does not change based on previous outcomes.
Based on these results, the probability that the next flip results in tails cannot be determined from the past results of flipping the coin 100 times. Coin tosses are independent events, meaning the outcome of one toss does not affect the outcome of another. In theory, a fair coin has a 50 percent chance of landing on either heads or tails on any given flip, regardless of previous results. So, even though the student observed 71 heads and 29 tails, the probability of the next flip resulting in tails is still 0.5 or 50%.
This illustrates the concept of the law of large numbers, which states that as the number of trials increases, the experimental probability will get closer to the theoretical probability. But for any individual toss, the probability remains unchanged at 50 percent for either outcome. Karl Pearson's experiment of tossing a fair coin 24,000 times supports this, where he nearly reached an equal number of heads and tails, highlighting the consistency of probability in the long run.