Final answer:
The inquiry pertains to the area of probability, focusing on sample spaces and mutually exclusive events in the context of rolling dice and tossing coins. It addresses the calculation of event probabilities and the mutual exclusivity of events A and B as well as A and C.
Step-by-step explanation:
The subject in question is related to the concept of probabilities and sample spaces in events involving rolling a die and tossing a coin. The sample space for a single die and a coin is given by the product of possible outcomes from each: there are 6 outcomes for the die (1 through 6) and 2 outcomes for the coin (Heads or Tails). Therefore, there are 12 possible outcomes in total which can be listed as H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, and T6 (where the first letter stands for the coin outcome and the number stands for the die outcome).
Event A, where either a three or a four is rolled followed by landing a head on the coin toss, includes outcomes H3 and H4. The probability of event A, denoted as P(A), can be calculated by dividing the number of favorable outcomes for A by the total number of outcomes in the sample space, yielding P(A) = 2/12 or 1/6. Events that are mutually exclusive are those that cannot occur at the same time. In this case, if event B is defined as landing heads on the first and second toss, it cannot occur simultaneously with A (rolling a 3 or 4 on a die and then a head on the coin), so they are mutually exclusive. However, event C, which includes outcomes when a red or blue card is involved, is not mutually exclusive with event A, because event C includes all outcomes of event A (assuming there's a component of the experiment involving cards that can be either red or blue).