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In a school, [tex]$40 \%$[/tex] of the students have brown eyes. Find the experimental probability that in a group of 4 students, at least one of them has brown eyes. The problem has been simulated by generating random numbers. The digits [tex]$0 - 9$[/tex] were used. Let numbers "0", "1", "2", and "3" represent the [tex]$40 \%$[/tex] of students with brown eyes. A sample of 20 random numbers is shown.

[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
7918 & 7910 & 2546 & 1390 & 6075 \\
\hline
1230 & 2386 & 0793 & 7359 & 3048 \\
\hline
2816 & 6147 & 5978 & 5621 & 9732 \\
\hline
9436 & 3806 & 5971 & 6173 & 1430 \\
\hline
\end{tabular}
\][/tex]

Experimental Probability [tex]$=[?] \%$[/tex]

Sagot :

GinnyAnsweridn
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].
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