Final answer:
The probability that event F (rolling a four or five) occurs for the first time on the second trial is calculated using geometric distribution, with p being 1/3 and q being 2/3, resulting in a probability of 2/9.
Step-by-step explanation:
The subject discussed is geometric distribution, a concept in probability theory often covered in high school mathematics. According to the problem, we are dealing with an event F (rolling a four or five) and are required to calculate the probability that this event occurs for the first time on the second trial. To calculate this probability (p), we must first understand that geometric distribution describes the number of trials up until the first success, with the probability of success being denoted by p and the probability of failure by q, where q = 1 - p.
Let's define the following for the event F: