-{13}, 4, 23 A data set of three numbers is shown. If a number from this data set is selected...

1. TRANSLATE the problem information

• Given information:
  • Data set: \(-13, 4, 23\)
  • Need to find probability of selecting a negative number at random

• What this means: We need to count negative numbers and divide by total numbers

2. INFER which numbers are negative

• Check each number against zero:
  • \(-13\): This is less than 0, so it's negative ✓
  • 4: This is greater than 0, so it's positive
  • 23: This is greater than 0, so it's positive

• Result: 1 negative number out of 3 total numbers

3. Apply the probability formula

• \(\mathrm{P(negative\,number)} = \frac{\mathrm{count\,of\,negative\,numbers}}{\mathrm{total\,count}}\)
• \(\mathrm{P(negative\,number)} = \frac{1}{3}\)

Answer: B. 1/3

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about negative numbers: Some students incorrectly identify which numbers are negative, possibly thinking that any number could be negative or confusing negative with positive.

For example, they might mistakenly count 4 and 23 as negative numbers, leading to \(\mathrm{P} = \frac{2}{3}\). This may lead them to select Choice C (2/3).

Second Most Common Error:

Weak TRANSLATE skill: Students might misunderstand what "probability of selecting a negative number" means and instead calculate the probability of selecting a positive number.

Since there are 2 positive numbers out of 3, they calculate \(\mathrm{P} = \frac{2}{3}\). This may lead them to select Choice C (2/3).

The Bottom Line:

This problem tests whether students can correctly identify negative numbers and apply basic probability concepts. The key insight is systematically checking each number in the data set against zero to determine which are negative.