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Which algorithm can be used to select and display the names of 2 students at random from a group of 30 students in a classroom?

Updated January 5, 2025

A teacher has a goal of displaying the names of 2 students selected at random from a group of 30 students in a classroom. Any possible pair of students should be equally likely to be selected. Which of the following algorithms can be used to accomplish the teacher’s goal?

A)
Step 1: Assign each student a unique integer from 1 to 30.
Step 2: Generate a random integer n from 1 to 15.
Step 3: Select the student who is currently assigned integer n and display the student’s name.
Step 4: Generate a new random integer from 16 to 30.
Step 5: Select the student who is currently assigned integer n and display the student’s name.

B)
Step 1: Assign each student a unique integer from 1 to 30.
Step 2: Generate a random integer from 1 to 30.
Step 3: Select the student who is currently assigned integer n and display the student’s name.
Step 4: Generate a new random integer from 1 to 30.
Step 5: Select the student who is currently assigned integer n and display the student’s name.

C)
Step 1: Assign each student a unique integer from 1 to 30.
Step 2: Generate a random odd integer from 1 to 29.
Step 3: Select the student who is currently assigned integer n and display the student’s name.
Step 4: Generate a new random even integer from 2 to 30.
Step 5: Select the student who is currently assigned integer n and display the student’s name.

1 Answer

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Quizzma TeamJanuary 5, 2025

The correct answer is A).

Explanation:

Option A utilizes a method that ensures that both selected students can be different and equally likely by generating random integers from non-overlapping ranges. It selects one student from 1 to 15 and another from 16 to 30, which minimizes the chance of selecting the same student twice, ensuring variety in selection.

Options B and C do not achieve true random and unique selections effectively. Option B could potentially select the same student twice since both random integers are drawn from the same range. Option C restricts the selection of students to odd and even integers, which means some students will never be chosen if they are not odd or even, reducing the total possible selections.

Therefore, option A is the best algorithm to achieve the teacher’s goal!