Let's examine the results of Raul's simulation and determine the validity of the given statements step-by-step.
First, we summarize the information we know from the simulation results.
### Simulation Results
The outcomes of the 15 experiments are:
- HTH, HHH, TTT, HTT, HHT
- TTT, HTT, HTT, HTT, HHH
- HHT, HTT, TTT, TTT, HTH
From these results, Raul determines:
1. The total number of experiments performed.
2. The number of successful series, where success is defined as winning all three games ('HHH').
3. The number of series that include at least one head 'H'.
### Step-by-Step Analysis
1. Determine the number of experiments performed:
- There are a total of 15 results listed.
- Hence, the number of experiments performed is [tex]\( \textbf{15} \)[/tex].
2. Determine the number of successes:
- Raul wins all three games (which we consider a success) if he gets 'HHH'.
- From the simulation results, 'HHH' appears exactly 2 times.
- Thus, the number of successes is [tex]\( \textbf{2} \)[/tex].
3. Determine the number of series that include at least one head (H):
- Any sequence that contains at least one 'H' meets this criterion.
- The simulation contains the following series with at least one 'H': HTH, HHH, HTT, HHT, HTT, HTT, HTT, HHH, HHT, HTH
- Counting these, we have [tex]\( \textbf{11} \)[/tex] series that include at least one 'H'.
4. Length of each experiment:
- Each result in the given simulation consists of three coin tosses (3 characters per result).
- Therefore, every experiment includes three coin tosses.
### Verification of Statements
Let's verify each given statement based on our analysis:
- Statement A: "There were two successes."
- From our analysis, this is correct. There are exactly 2 successes (HHH).
- Statement B: "A series of 15 experiments were performed."
- From our summary, this is correct. There are 15 experiments performed.
- Statement C: "The successes are all the experiments that include at least one head."
- From our analysis, this is incorrect. Success is defined as 'HHH', but there are 11 experiments that include at least one 'H'. Only 2 out of these 11 are 'HHH' which is a success. So, the successes are not all the experiments that include at least one head.
- Statement D: "Each experiment includes three coin tosses."
- From our analysis, this is correct. Each experiment consists of three coin flips.
### Conclusion
The false statement from the options given is:
- Statement C: The successes are all the experiments that include at least one head.
Hence, the statement which is not true is:
C. The successes are all the experiments that include at least one head.
