Final answer:
The question asks for the optimal bet size to maximize long-run expected earnings when betting on a fair coin toss. The Kelly criterion is implied for such calculations, however, without a direct mention in the supporting information. A referral to study the Kelly criterion is recommended.
Step-by-step explanation:
The question involves determining the optimal bet size when betting on a fair coin toss with the chance to win 1.2 times the bet amount. This problem is rooted in probability theory and expected value calculations, which are mathematical concepts used to evaluate the long-run average results of random events. In this case, the optimal bet would maximize the expected value of the game.
However, to calculate the optimal bet size, one would typically use the Kelly criterion, which maximizes the expected logarithm of wealth and is a well-known formula in the contexts of gambling and financial investment. This formula is not directly provided in the supporting information and requires knowledge of the probability of winning (which is 0.5 for a fair coin), the net odds received on the wager (0.2 in this case, as you receive 1.2 times the bet), and the probability of losing (also 0.5).
To ensure accuracy in such an advising scenario, without explicit instructions or formula for the optimal bet size calculation, it's recommended to refer the student to study the Kelly criterion or consult a resource that explains how to apply this concept.