What is the sample space for rolling a fair six-sided die and flipping a fair coin?
To determine the sample space for rolling a fair six-sided die and flipping a fair coin, we need to consider all the possible outcomes for each event and then combine them.
First, let's start with rolling the six-sided die. The possible outcomes for this event are the numbers 1, 2, 3, 4, 5, and 6.
Next, we move on to flipping the coin. Since it's a fair coin, there are two possible outcomes: heads or tails.
To find the sample space, we need to consider all the combinations of these two events. We can pair each number on the die with each outcome of the coin flip. For example, if we roll a 1 on the die and flip heads, one outcome is (1, H). Similarly, if we roll a 1 on the die and flip tails, another outcome is (1, T). We can do this for all the numbers on the die and both outcomes of the coin flip.
So, the sample space for rolling a fair six-sided die and flipping a fair coin consists of 6 possible outcomes from the die (1, 2, 3, 4, 5, 6) paired with 2 possible outcomes from the coin flip (H, T), resulting in a total of 12 possible outcomes:
{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}