Final answer:
The size of the sample space for a coin toss experiment is determined by raising 2 to the power of the number of tosses. For a combination of a die roll and a coin toss, the sample space size is the product of the outcomes from each (12 in this case).
Step-by-step explanation:
Understanding the Sample Space for Coin Tosses
When considering the experiment of tossing a single fair coin, there are two possible outcomes: a head (H) or a tail (T). For each additional coin toss, the number of possible outcomes doubles, since each toss is independent and has two possible outcomes. Therefore, if we want to determine the sample space for a given number of tosses, we simply calculate 2 raised to the power of the number of tosses, which is expressed mathematically as 2^n where n is the number of coin tosses. For example, with three coin tosses, the sample space is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, which yields 2^3 = 8 different outcomes.
When tossing a fair six-sided die followed by a coin toss, the sample space consists of combining each die outcome (1 through 6) with each coin outcome (H or T). Multiply the two numbers of outcomes for the die (6) and the coin (2) to find the number of outcomes for the combined experiment, giving us a sample space size of 6 * 2 = 12 outcomes. These outcomes include the combinations like H1, T6, among others.