Select the correct answer.

A fair, unbiased coin was flipped 10 times, giving the results shown in the table, where [tex]$T =$[/tex] tails and [tex]$H =$[/tex] heads.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Flip & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Result & T & T & T & H & T & T & T & H & T & T \\
\hline
\end{tabular}

What is the difference between the theoretical and empirical probabilities of getting heads?

A. 0.5
B. 0.3
C. 0.0
D. 0.1



Answer :

Let's solve the problem step by step.

1. Identify the theoretical probability:
- For a fair coin, the probability of getting heads (H) is always \(0.5\). This is the theoretical probability.

2. Count the number of heads (H) observed in the 10 flips:
- From the table, let's count the occurrences of heads.
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline Flip & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Result & T & T & T & H & T & T & T & H & T & T \\ \hline \end{array} \][/tex]
- Heads appear in the 4th and 8th flips, so we observed heads 2 times.

3. Determine the total number of flips:
- The coin was flipped 10 times in total.

4. Calculate the empirical probability of getting heads:
- The empirical probability is given by the ratio of the number of heads observed to the total number of flips.
[tex]\[ \text{Empirical Probability} = \frac{\text{Number of Heads}}{\text{Total Number of Flips}} = \frac{2}{10} = 0.2 \][/tex]

5. Find the difference between the theoretical and empirical probabilities:
- Theoretical Probability of Heads = \(0.5\)
- Empirical Probability of Heads = \(0.2\)
- The difference between the theoretical and empirical probabilities is:
[tex]\[ \text{Difference} = |0.5 - 0.2| = 0.3 \][/tex]

So, the correct answer is:
[tex]\[ \boxed{0.3} \][/tex]

Therefore, the answer is option B: 0.3.