The problem asks us to determine the total number of possible outcomes in an experiment involving coin flips with different conditions depending on the first flip.

Here's how the experiment works:

1. A coin is flipped once.
2. If the first flip is heads, the coin is flipped 3 more times (a total of 4 flips).
3. If the first flip is tails, the coin is flipped 2 more times (a total of 3 flips).

Solution:

• Each flip of the coin has two possible outcomes: heads (H) or tails (T).

1. If the first flip is heads (H), there will be 3 additional flips, resulting in a total of 4 flips. Since each flip has 2 outcomes, the total number of outcomes for this case is: $2^4 = 16 \text{ outcomes}.$

2. If the first flip is tails (T), there will be 2 additional flips, resulting in a total of 3 flips. The total number of outcomes for this case is: $2^3 = 8 \text{ outcomes}.$

Total Outcomes:

The total number of outcomes in the sample space is the sum of both cases: $16 \ (\text{if heads first}) + 8 \ (\text{if tails first}) = 24 \ \text{outcomes}.$

Thus, the sample space for this experiment consists of 24 possible outcomes.

Would you like more details on how to visualize these outcomes or have any further questions?

Here are 5 related questions for further exploration:

1. How would the outcome change if the coin had more sides, like a three-sided coin?
2. What if instead of flipping a coin, you roll a die with similar conditions?
3. How does this experiment relate to probability calculations for each possible outcome?
4. What would happen if the number of flips after the first heads or tails was different?
5. How can we compute the probability of getting exactly two heads in this experiment?

Tip: To calculate possible outcomes in multi-stage experiments, break down the scenario step-by-step, as each decision point influences the total outcomes.