Final answer:
In an experiment where a coin is tossed multiple times, the relative frequency of tails (or heads) is the number of times tails (or heads) occurs divided by the total number of tosses. As the number of tosses increases, the relative frequency should approach 0.5, provided the coin is fair. This is based on the law of large numbers, illustrating that experimental results align more closely with predicted probabilities over many repetitions.
Step-by-step explanation:
In order to perform the experiment of tossing a coin and compute the probability of observing a tail using relative frequency, we first need to define the relative frequency as the number of times a specific outcome occurs divided by the total number of trials. For example, if we perform an experiment and toss a coin 100 times and get tails 45 times, the relative frequency of tails would be 45/100 = 0.45.
To observe the long-term effects of this type of experiment, you would expect to approach a relative frequency of 0.5 for tails as the number of trials increases, as long as the coin is fair. This is due to the law of large numbers which states that as the number of trials in an experiment is increased, the relative frequency obtained in the experiment tends to come closer to the theoretical probability.
This concept was demonstrated by Karl Pearson who tossed a coin 24,000 times and obtained a relative frequency of heads of 12,012/24,000 = .5005 which is very close to the theoretical probability of 0.5.
Learn more about Probability and Relative Frequency