Select the correct answer.

A fair, unbiased coin was flipped 10 times, giving the results shown in the table, where [tex]\( T \)[/tex] denotes tails and [tex]\( H \)[/tex] denotes 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 experimental probabilities of getting heads?

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



Answer :

To find the difference between the theoretical and experimental probabilities of getting heads, we can follow a step-by-step process:

1. Count the total number of flips:
The total number of flips is given as 10.

2. Count the number of heads (H):
From the table, we observe the results: T, T, T, H, T, T, T, H, T, T.
There are 2 heads in the given sequence.

3. Calculate the experimental probability of getting heads:
The experimental probability is given by the formula:
[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Heads}}{\text{Total Number of Flips}} \][/tex]
Substituting the values, we get:
[tex]\[ \text{Experimental Probability} = \frac{2}{10} = 0.2 \][/tex]

4. Determine the theoretical probability of getting heads:
For a fair, unbiased coin, the probability of getting heads is always 0.5.

5. Calculate the difference between the theoretical and experimental probabilities:
The difference can be calculated by taking the absolute value of the difference between the theoretical and experimental probabilities:
[tex]\[ \text{Difference} = |0.5 - 0.2| = 0.3 \][/tex]

Thus, the difference between the theoretical and experimental probabilities of getting heads is [tex]\( \boxed{0.3} \)[/tex]. So, the correct answer is:
[tex]\[ \text{B.} \quad 0.3 \][/tex]