Sure! Let’s go through the solution step-by-step, based on the problem presented:
### (1) Construct a Frequency Table for the Data:
The table provided shows the outcomes and their respective frequencies of the spins. Here is the frequency table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Outcome} & \text{Number of Spins} \\
\hline
1 & 13 \\
2 & 9 \\
3 & 24 \\
4 & 7 \\
5 & 11 \\
6 & 8 \\
7 & 10 \\
8 & 5 \\
9 & 7 \\
10 & 6 \\
\hline
\end{array}
\][/tex]
### (2) Experimental Probability of Spinning a 5:
The experimental probability of spinning a number is the number of times that outcome occurs divided by the total number of spins. Here, we want the probability of spinning a 5.
Number of spins of 5 = 11 \
Total number of spins = 100
So,
[tex]\[
\text{Experimental Probability of spinning a 5} = \frac{11}{100} = 0.11
\][/tex]
### (3) Experimental Probability of Spinning a 3:
Similarly, we calculate the probability of spinning a 3.
Number of spins of 3 = 24 \
Total number of spins = 100
So,
[tex]\[
\text{Experimental Probability of spinning a 3} = \frac{24}{100} = 0.24
\][/tex]
### (4) Experimental Probability of Spinning a Multiple of 2:
The multiples of 2 in the given outcomes are 2, 4, 6, 8, and 10.
Number of spins of 2 = 9 \
Number of spins of 4 = 7 \
Number of spins of 6 = 8 \
Number of spins of 8 = 5 \
Number of spins of 10 = 6
Total number of spins for multiples of 2 = 9 + 7 + 8 + 5 + 6 = 35 \
Total number of spins = 100
So,
[tex]\[
\text{Experimental Probability of spinning a multiple of 2} = \frac{35}{100} = 0.35
\][/tex]
### (5) Experimental Probability of Spinning a Number Below 6:
The numbers below 6 are 1, 2, 3, 4, and 5.
Number of spins of 1 = 13 \
Number of spins of 2 = 9 \
Number of spins of 3 = 24 \
Number of spins of 4 = 7 \
Number of spins of 5 = 11
Total number of spins for numbers below 6 = 13 + 9 + 24 + 7 + 11 = 64 \
Total number of spins = 100
So,
[tex]\[
\text{Experimental Probability of spinning a number below 6} = \frac{64}{100} = 0.64
\][/tex]
### (6) Theoretical Probability of Spinning a 2:
In a 10-sector spinner, each outcome is equally likely. Hence, the theoretical probability of any specific outcome (such as spinning a 2) is:
[tex]\[
\text{Theoretical Probability of spinning a 2} = \frac{1}{10} = 0.1
\][/tex]
In summary:
1. Frequency table is as provided.
2. Experimental probability of spinning a 5: [tex]\(0.11\)[/tex]
3. Experimental probability of spinning a 3: [tex]\(0.24\)[/tex]
4. Experimental probability of spinning a multiple of 2: [tex]\(0.35\)[/tex]
5. Experimental probability of spinning a number below 6: [tex]\(0.64\)[/tex]
6. Theoretical probability of spinning a 2: [tex]\(0.1\)[/tex]
These answers match the data you've provided and should be helpful for your understanding!
