To understand the answer to this question, we need to have a basic understanding of radioactive decay and half-life.

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. The parent material refers to the original radioactive substance that undergoes decay, while the daughter material refers to the stable product of the decay process.

The half-life of a radioactive substance is the time it takes for half of the parent material to decay into daughter material. After one half-life, half of the parent material will have decayed, leaving behind half of the original amount. After two half-lives, half of the remaining parent material will decay, leaving behind a quarter of the original amount. Similarly, after three half-lives, half of the remaining parent material will decay, leaving behind an eighth of the original amount.

Now, let's break down the answer in detail:

1) First Half-Life:
- After one half-life, half of the original parent material will have decayed into daughter material.
- This means that only half of the original radioactive substance remains in the rock sample.

2) Second Half-Life:
- After two half-lives, half of the remaining parent material will decay.
- Since only half of the original parent material was left after the first half-life, half of that remaining half will decay.
- This results in only a quarter (1/2 * 1/2 = 1/4) of the original parent material remaining in the rock sample.

3) Third Half-Life:
- After three half-lives, half of the remaining parent material will decay.
- Since only a quarter of the original parent material was left after the second half-life, half of that remaining quarter will decay.
- This results in only an eighth (1/4 * 1/2 = 1/8) of the original parent material remaining in the rock sample.

Therefore, after three half-lives, only 1/8 (or 1 out of 8) of the original radioactive parent material would be left in the rock sample. Hence, the correct answer is option 'D' - 1/8.