an experiment consistbnof tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4H, for example to denote an event that die comes up 4 and then the coin comes up heads, and 3HT to denote another event that the die comes up 3 followed by a head and a tail on the coin, list 18 elements of the sample space.

To list the elements of the sample space, we need to consider all possible outcomes of the experiment.

Step 1: Identify the possible outcomes of rolling the die: The die has 6 sides, numbered 1 to 6.

Step 2: Determine the number of coin flips based on the outcome of the die:
- If the number on the die is even (2, 4, or 6), we flip the coin once.
- If the number on the die is odd (1, 3, or 5), we flip the coin twice.

Step 3: Combine the outcomes of the die and the coin flips to form the elements of the sample space.

Sample space elements:
1H, 1HT, 1TH
2H, 2HT, 2TH
3H, 3HH, 3HT, 3TH, 3TT
4H, 4HT, 4TH
5H, 5HH, 5HT, 5TH, 5TT
6H, 6HT, 6TH

So, the sample space consists of 18 elements.