The problem asks for the total number of possible outcomes in a coin-flipping experiment with specific conditions.

Let's break it down step by step:

1. Initial Flip:

   • The coin is flipped once. There are two possible outcomes: either heads (H) or tails (T).

2. If the first flip is heads (H):

   • The coin is flipped 4 more times.
   • Each flip has two possible outcomes (heads or tails).
   • Since there are 4 flips and each flip has 2 outcomes, the number of possible outcomes for this branch is $2^4 = 16$.

3. If the first flip is tails (T):

   • The coin is flipped 2 more times.
   • Each of these flips also has two possible outcomes.
   • Therefore, the number of possible outcomes for this branch is $2^2 = 4$.

Total Sample Space:

• From the first flip, we have two branches:
  1. If heads (H), there are 16 outcomes.
  2. If tails (T), there are 4 outcomes.

Thus, the total number of possible outcomes is: $2^4 + 2^2 = 16 + 4 = 20$

Therefore, the total number of possible outcomes in the sample space is 20.

Let me know if you need any further details or explanations!

Related Questions:

1. What is the probability of flipping exactly 2 heads in the case where the first flip is heads?
2. How would the sample space change if there were 3 flips after tails instead of 2?
3. What is the total number of outcomes if there were 5 flips regardless of the result of the first flip?
4. How many outcomes contain at least 3 heads in the case of 4 additional flips?
5. What would be the sample space if the second flip was also dependent on the outcome of the first flip?

Tip: In coin-flipping problems, always identify how many independent flips occur, as this allows you to calculate the total number of possible outcomes.