To determine the experimental probability of rolling a 6 on a number cube based on the given experimental results, we can follow these steps:
1. Understand the Data: We are given the frequencies of each outcome (the number of times each number appeared) when the number cube was rolled:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline \text{Number} & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline \text{Frequency} & 13 & 11 & 9 & 8 & 10 & 9 \\
\hline
\end{array}
\][/tex]
2. Calculate the Total Number of Rolls:
To find the total number of rolls, we sum up all the frequencies:
[tex]\[
\text{Total Rolls} = 13 + 11 + 9 + 8 + 10 + 9 = 60
\][/tex]
3. Find the Frequency of Rolling a 6:
From the table, the frequency of rolling a 6 is given as 9.
4. Calculate the Experimental Probability:
The experimental probability [tex]\(P\)[/tex] of rolling a 6 is given by the ratio of the frequency of rolling a 6 to the total number of rolls. Mathematically, this is expressed as:
[tex]\[
P(\text{rolling a 6}) = \frac{\text{Frequency of 6}}{\text{Total Rolls}}
\][/tex]
Substituting the values we have:
[tex]\[
P(\text{rolling a 6}) = \frac{9}{60}
\][/tex]
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
P(\text{rolling a 6}) = \frac{9 \div 3}{60 \div 3} = \frac{3}{20}
\][/tex]
Converting this fraction to a decimal gives:
[tex]\[
P(\text{rolling a 6}) = 0.15
\][/tex]
Therefore, the experimental probability of rolling a 6 is [tex]\(0.15\)[/tex] or [tex]\(15\%\)[/tex].
