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Of the students at Creekview Middle School, [tex]30\%[/tex] are in 6th grade, [tex]30\%[/tex] are in 7th grade, and [tex]40\%[/tex] are in 8th grade. What is the estimated probability that at least one of the next three students entering the school will be a 6th grader?

Here are the results of a simulation using a random number generator:
- Let [tex]1, 2, 3 = 6[/tex]th grader
- Let [tex]4, 5, 6 = 7[/tex]th grader
- Let [tex]7, 8, 9, 0 = 8[/tex]th grader

\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline Group number & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline Random digits & 602 & 433 & 791 & 398 & 041 & 209 & 467 & 570 & 221 & 407 \\
\hline
\end{tabular}

Which of the 10 groups show at least one 6th grader?

A. 1, 7
B. 7, 8, 10
C. 1, 2, 3, 4, 5, 6, 9
D. 1, 2, 5, 7, 8, 10



Answer :

GinnyAnswer
To determine which groups contain at least one 6th grader, we need to identify groups that have at least one of the digits 1, 2, or 3.

Here is a step-by-step breakdown of each group:

1. Group 1: 602
- Contains the digit 2 (6th grader).
- Group 1 has a 6th grader.

2. Group 2: 433
- Contains the digit 3 (6th grader).
- Group 2 has a 6th grader.

3. Group 3: 791
- Contains the digit 1 (6th grader).
- Group 3 has a 6th grader.

4. Group 4: 398
- Contains the digit 3 (6th grader).
- Group 4 has a 6th grader.

5. Group 5: 041
- Contains the digit 1 (6th grader).
- Group 5 has a 6th grader.

6. Group 6: 209
- Contains the digit 2 (6th grader).
- Group 6 has a 6th grader.

7. Group 7: 467
- Does not contain the digits 1, 2, or 3 (no 6th graders).
- Group 7 does not have a 6th grader.

8. Group 8: 570
- Does not contain the digits 1, 2, or 3 (no 6th graders).
- Group 8 does not have a 6th grader.

9. Group 9: 221
- Contains the digits 2 and 1 (6th graders).
- Group 9 has a 6th grader.

10. Group 10: 407
- Does not contain the digits 1, 2, or 3 (no 6th graders).
- Group 10 does not have a 6th grader.

Based on this analysis, the groups that contain at least one 6th grader are:
- Group 1
- Group 2
- Group 3
- Group 4
- Group 5
- Group 6
- Group 9

Therefore, the correct answer is:

C. 1, 2, 3, 4, 5, 6, 9

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