Final answer:
The question pertains to sample spaces and probabilities in flipping three fair coins. We create a sample space with all possible outcomes and calculate the probabilities for the number of heads. This study of probability forms part of High School Mathematics.
Step-by-step explanation:
The subject of this question is Mathematics, specifically within the study of probability. When flipping three fair coins, we can create a sample space, which lists all possible outcomes: TTT, THH, HTH, HHT, HTT, THT, TTH, HHH. Each combination represents a different outcome of the three coin tosses, with T for tails and H for heads. For example, THH indicates that the first coin landed tails and the other two landed heads.
The number of heads (X) that result from these coin tosses can vary; X can be 0, 1, 2 or 3. We count the number of heads in each outcome of the sample space to determine the probability distribution of X. With one head being THT, TTH, or HTT, two heads being THH, HTH, or HHT, and three heads being HHH. The probability of each can be calculated by dividing the number of outcomes with the corresponding heads by the total number of outcomes in the sample space.
When looking at games or experiments involving coins, dice, and other random devices, we must consider the probabilities of each outcome, the design of the game, and whether certain outcomes are mutually exclusive or independent when analyzing potential results or calculating expected values.