Certainly! Let's break down the solution step-by-step:
1. Identify the Given Data:
- We are given the results of three trials of tossing an unbiased coin 10 times each.
- The trials are:
- Trial 1: TTHHTHTTHH
- Trial 2: TTTTTHHHHH
- Trial 3: THTHHHTTHT
2. Total Tosses:
- Each trial consists of 10 tosses.
- With 3 trials, the total number of tosses is:
[tex]\[
3 \times 10 = 30
\][/tex]
3. Count the Number of Heads:
- From Trial 1 (TTHHTHTTHH), the count of heads (H) is 5.
- From Trial 2 (TTTTTHHHHH), the count of heads (H) is 5.
- From Trial 3 (THTHHHTTHT), the count of heads (H) is 5.
- Combining these results, the total number of heads over all trials is:
[tex]\[
5 + 5 + 5 = 15
\][/tex]
4. Experimental Probability of Getting Heads:
- The experimental probability is calculated by dividing the total number of heads by the total number of tosses:
[tex]\[
\text{Experimental Probability of Heads} = \frac{\text{Number of Heads}}{\text{Total Number of Tosses}} = \frac{15}{30} = 0.5
\][/tex]
5. Theoretical Probability of Getting Heads:
- For a single unbiased coin toss, the probability of landing heads (H) is theoretically 0.5.
6. Calculate the Difference:
- To find the difference between the theoretical and experimental probabilities of getting heads:
[tex]\[
\text{Difference} = \left| \text{Theoretical Probability} - \text{Experimental Probability} \right| = \left| 0.5 - 0.5 \right| = 0.0
\][/tex]
Therefore, the difference between the theoretical and experimental probabilities of getting heads is [tex]\(0.0\)[/tex].
