Let's solve the problem step by step.
1. Count the total number of digits:
We have 20 random 4-digit numbers. Each number contributes 4 digits.
[tex]\[
\text{Total number of digits} = 20 \times 4 = 80
\][/tex]
2. Extract the digits from the 20 random numbers provided:
[tex]\[
\begin{aligned}
7918 &:\ 7, 9, 1, 8 \\
7910 &:\ 7, 9, 1, 0 \\
2546 &:\ 2, 5, 4, 6 \\
1390 &:\ 1, 3, 9, 0 \\
6075 &:\ 6, 0, 7, 5 \\
1230 &:\ 1, 2, 3, 0 \\
2386 &:\ 2, 3, 8, 6 \\
0793 &:\ 0, 7, 9, 3 \\
7359 &:\ 7, 3, 5, 9 \\
3048 &:\ 3, 0, 4, 8 \\
2816 &:\ 2, 8, 1, 6 \\
6147 &:\ 6, 1, 4, 7 \\
5978 &:\ 5, 9, 7, 8 \\
5621 &:\ 5, 6, 2, 1 \\
9732 &:\ 9, 7, 3, 2 \\
9436 &:\ 9, 4, 3, 6 \\
3806 &:\ 3, 8, 0, 6 \\
5971 &:\ 5, 9, 7, 1 \\
6173 &:\ 6, 1, 7, 3 \\
1430 &:\ 1, 4, 3, 0 \\
\end{aligned}
\][/tex]
3. Identify the digits representing students with brown eyes:
The digits 0, 1, 2, and 3 represent the [tex]$40\%$[/tex] of students with brown eyes.
4. Count the number of digits that are 0, 1, 2, or 3:
[tex]\[
\begin{aligned}
\text{Digits} &:\ [7, 9, 1, 8, 7, 9, 1, 0, 2, 5, 4, 6, 1, 3, 9, 0, 6, 0, 7, 5, 1, 2, 3, 0, 2, 3, 8, 7, 0, 7, 9, 3, 7, 3, 5, 9, 3, 0, 4, 8, 2, 8, 1, 6, 6, 1, 4, 7, 5, 9, 7, 8, 5, 6, 2, 1, 9, 7, 3, 2, 9, 4, 3, 6, 3, 8, 0, 6, 5, 9, 7, 1, 6, 1, 7, 3, 1, 4, 3, 0] \\
& = [1, 0, 2, 1, 3, 0, 1, 2, 3, 0, 0, 3, 3, 2, 2, 0, 1, 1, 3, 2, 3, 0, 2, 1, 3] \\
\end{aligned}
\][/tex]
Total count of brown eye digits = [tex]\( 3 (0's) + 7 (1's) + 6 (2's) + 9 (3's) = 25 \)[/tex]
5. Calculate the experimental probability:
Experimental Probability is calculated by dividing the number of favorable outcomes (digits representing brown eyes) by the total number of digits and then multiplying by 100 to express it as a percentage.
[tex]\[
\text{Experimental Probability} = \left( \frac{\text{Number of digits with 0, 1, 2, or 3}}{\text{Total Number of digits}} \right) \times 100
\][/tex]
[tex]\[
\text{Experimental Probability} = \left( \frac{25}{80} \right) \times 100 = 31.25 \%
\][/tex]
Therefore, the experimental probability that in a group of 4 students, at least one of them has brown eyes is [tex]\(31.25\%\)[/tex].
