To solve this problem, we need to determine the number of possible outcomes in the sample space for the coin-flipping experiment.

Step-by-Step Breakdown:

1. Initial Flip:

   • The first flip determines two branches: either a heads (H) or a tails (T).

2. If Heads is Flipped on the Initial Flip:

   • The coin is flipped 5 more times, and we are interested in the number of heads flipped in these 5 flips.
   • Each flip can result in either heads or tails, so there are $2^5 = 32$ possible outcomes for the 5 flips following the initial heads.

3. If Tails is Flipped on the Initial Flip:

   • The coin is flipped 4 more times, and we record the result of each individual flip.
   • Since each flip has 2 possible outcomes (heads or tails), the number of possible outcomes for these 4 flips is $2^4 = 16$.

4. Total Sample Space:

   • The initial flip has 2 possible outcomes (heads or tails).
   • If the initial flip is heads, there are 32 possible outcomes.
   • If the initial flip is tails, there are 16 possible outcomes.

   Therefore, the total number of possible outcomes in the sample space is: $2 \times (32 + 16) = 2 \times 48 = 96$

Thus, the total number of possible outcomes in the sample space of this experiment is 96.

---

Would you like further explanation or details on any part of this solution?

Here are five related questions to deepen your understanding:

1. How would the solution change if we flipped the coin 6 times instead of 5 after the initial heads?
2. What if the coin used was biased, and heads had a different probability than tails?
3. How many outcomes would there be if both the heads and tails paths involved 5 additional flips?
4. What is the probability of getting exactly 3 heads in the 5 additional flips after flipping heads initially?
5. How does this problem relate to binomial distributions?

Tip: When solving probability problems, always carefully consider the different branches or stages of the experiment. Each branch multiplies the number of possible outcomes.