You and a friend are talking about the probability of getting a heads on a single toss of a fair coin. Your friend insists that you are more likely to get a heads on a single toss of a fair coin than a tails. Is your friend correct, why or why not? If we were to toss the fair coin an infinite number of times, what would we expect?

The probability of getting a heads on a single toss of a fair coin is not influenced by previous tosses, and it remains constant at 0.5 or 50%. Therefore, your friend’s assertion that getting a heads is more likely than getting a tails on a single toss is incorrect.

In order to understand why this is the case, let us first define a fair coin. A fair coin is a coin that has an equal probability of landing on either heads or tails. Hence, on a single toss of a fair coin, there are only two possible outcomes: heads or tails.

The probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes. In the case of a fair coin, there is only one favorable outcome (getting heads) out of the two possible outcomes (heads or tails). Therefore, the probability of getting a heads on a single toss is 1 out of 2, which can be represented as 1/2 or 0.5.

Furthermore, the probability of getting a heads or tails on each individual toss is mutually exclusive. This means that if we get a heads on one toss, the probability of getting a tails on the next toss remains the same (0.5). The outcome of each toss is independent of previous tosses.

Now, if we were to toss a fair coin an infinite number of times, what would we expect? Well, as the number of tosses approaches infinity, the relative frequency of getting heads or tails would approach the probability of each outcome. In this case, the relative frequency of getting heads would approach 0.5, as would the relative frequency of getting tails.

This phenomenon is known as the Law of Large Numbers, which states that as the number of trials increases, the relative frequency of the event approaches its true probability. In the case of a fair coin, the true probability of getting either heads or tails on each toss is 0.5.

To illustrate this concept, let’s assume we toss a fair coin 100 times. It is entirely possible to get a result such as 60 heads and 40 tails, which is not a perfect 50/50 split. However, as we increase the number of tosses to, say, 1000 or 10,000, the relative frequency of heads and tails would converge around 0.5, approaching the true probability.

In conclusion, the probability of getting a heads on a single toss of a fair coin is 0.5, and this probability remains constant regardless of previous tosses. If we were to toss the fair coin an infinite number of times, we would expect the relative frequency of getting heads or tails to approach 0.5, which is the true probability of each outcome.