Math Problem Statement

An elementary school teacher with 25 students plans to have each of them make a poster about two different states. The teacher first numbers the states​ (in alphabetical​ order, from 01 to​ 50), then uses a random number table to decide which states each kid gets. The random digits are  36660 10501 31850 24494

a) Which two state numbers does the first student​ get?

​b) Which two state numbers go to the second​ student?

Solution

Let's determine which state numbers each student receives using the given random digits sequence: 36660 10501 31850 24494.

a) Which two state numbers does the first student get?

The first student is assigned the first two valid pairs of digits from the sequence:

  1. 36 (First state)
  2. 66 is invalid since there is no state numbered 66. We skip it and move to the next valid pair.
  3. 60 is also invalid, so we skip it.
  4. 10 (Second state)

Answer for a: The first student gets states 36 and 10.

b) Which two state numbers go to the second student?

Next, we continue with the sequence to find the state numbers for the second student:

  1. 50 (First state)
  2. 01 (Second state)

Answer for b: The second student gets states 50 and 01.

Would you like more details or have any questions? Here are some related questions:

  1. How can we ensure every state is assigned at least once if students randomly select them?
  2. How does the probability distribution look if we were to use a different random sequence?
  3. What happens if the random number sequence repeats some state numbers?
  4. Can you describe a method to avoid assigning the same state to two students?
  5. How does the length of the random digit sequence impact the assignment process?
  6. What is the impact of the number of students on the assignment process?
  7. How could you design a fairer system that ensures all states are assigned equally?
  8. How would the assignment change if there were fewer than 50 states?

Tip: When using random numbers for assignments, always verify that the selected numbers fall within the required range and adjust as needed.

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Math Problem Analysis

Mathematical Concepts

Probability
Random Numbers
State Assignments

Formulas

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Theorems

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Suitable Grade Level

Elementary School