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 experimental probabilities of getting heads?

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



Answer :

Let's solve this problem step-by-step:

1. Count the number of heads (H) from the results:
Reviewing the given results: T, T, T, H, T, T, T, H, T, T.
We see heads (H) appear in the 4th and 8th flips.
Therefore, the number of heads (H) is 2.

2. Calculate the experimental probability of getting heads:
The experimental probability is calculated by dividing the number of times heads appears by the total number of flips.

[tex]\[ \text{Experimental Probability} = \frac{\text{Number of Heads}}{\text{Total Number of Flips}} = \frac{2}{10} = 0.2 \][/tex]

3. Determine the theoretical probability of getting heads for a fair coin:
A fair, unbiased coin has an equal chance of landing on heads or tails, so the theoretical probability of getting heads (H) is [tex]\(0.5\)[/tex] or [tex]\(50\%\)[/tex].

4. Find the difference between the theoretical and experimental probabilities:
The difference is found by subtracting the experimental probability from the theoretical probability:

[tex]\[ \text{Difference} = \left| \text{Theoretical Probability} - \text{Experimental Probability} \right| = \left| 0.5 - 0.2 \right| = 0.3 \][/tex]

So, the difference between the theoretical and experimental probabilities of getting heads is:

A. 0.3