Final answer:
When rolling a fair six-sided die, outcomes for different events can be defined and their corresponding probabilities calculated, but the true probability may only be observed over many trials, especially when considering potential biases in the die or coin.
Step-by-step explanation:
When you roll a fair six-sided die, the sample space is S = {1, 2, 3, 4, 5, 6}, representing all possible outcomes. For particular events, such as rolling an even number (event E), the outcomes are E = {2, 4, 6}. If event A is rolling a prime number, the outcomes are A = {2, 3, 5}, and if event B is rolling an odd number, then B = {1, 3, 5}. The intersection of events A and B (A AND B) consists of numbers that are both prime and odd, which yields {3, 5}, while the union of these events (A OR B) includes all numbers that are either prime or odd, resulting in {1, 2, 3, 5}. If the event of interest is rolling at least a five, the outcomes are {5, 6}, and the probability P(E) of this event is therefore 2/6, which simplifies to 1/3. Rolling the die a few times may not show the true probability due to the variability in short-term results, but in the long-term, such as after many rolls, the results should approach the theoretical probability. In situations where dice or coins may be unfair or biased, the outcomes might not be equally likely, and assessing such bias might require more repetitions of the experiment.