What is the sample space when rolling a fair six-sided die and flipping a fair coin?

To determine the sample space of rolling a fair six-sided die and flipping a fair coin, we need to consider all possible outcomes of both events.

The possible outcomes of rolling a six-sided die are represented by the numbers 1, 2, 3, 4, 5, and 6.

The possible outcomes of flipping a coin are represented by the two sides: heads and tails.

To find the sample space, we need to combine the possible outcomes of both events. Since they are independent events (rolling a die does not affect the outcome of flipping a coin, and vice versa), we can multiply the number of outcomes for each event.

Therefore, the sample space for rolling a six-sided die and flipping a coin is the set of all possible combinations of the two events, which can be represented as follows:

{1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T}

In this sample space, the first element of each combination represents the outcome of rolling the die, and the second element represents the outcome of flipping the coin.