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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.

Rework problem 29 from section 1.4 of your text, involving the flipping of a coin. A coin is flipped. If a heads is flipped, then the coin is flipped 4 more times and the number of heads flipped is noted; otherwise (i.e., tails is flipped on the initial flip), then the coin is flipped 2 more times and the result of each flip (i.e., heads or tails) is noted successively. How many possible outcomes are in the sample space of this experiment?

This problem explores the possible outcomes in a coin-flipping experiment with conditional flips based on the result of the first flip. Learn how to calculate the total outcomes in the sample space by understanding the branching structure of heads and tails flips.

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