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.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Flip & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
Result & T & T & T & H & T & T & T & H & T & T \\
\hline
\end{tabular}
\][/tex]

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

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



Answer :

To find the difference between the theoretical and experimental probabilities of getting heads, let's break down the problem step-by-step.

1. Counting the Heads:
- By examining the results, we observe that heads (H) appeared 2 times.

2. Total Number of Flips:
- The coin was flipped a total of 10 times.

3. Calculating the Experimental Probability of Getting Heads:
- The experimental probability of getting heads is the number of heads divided by the total number of flips.
[tex]\[ \text{Experimental Probability of Heads} = \frac{\text{Number of Heads}}{\text{Total Number of Flips}} = \frac{2}{10} = 0.2 \][/tex]

4. Theoretical Probability of Getting Heads:
- For a fair, unbiased coin, the theoretical probability of getting heads is 0.5 (since there are two equally likely outcomes—heads or tails).

5. Finding the Difference:
- Subtract the experimental probability from the theoretical probability.
[tex]\[ \text{Difference} = \text{Theoretical Probability} - \text{Experimental Probability} = 0.5 - 0.2 = 0.3 \][/tex]

Therefore, the correct answer is:

B. 0.3