-{11}, -{9}, 26 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: \(-11, -9, 26\)
  • Need to find probability of selecting a positive number at random
• What this tells us: We need to find what fraction of the numbers are positive

2. INFER the approach

• To find probability, we need: (number of positive numbers) ÷ (total numbers)
• First step: Identify which numbers are positive (greater than 0)

3. TRANSLATE each number's sign

• -11: negative (less than 0)
• -9: negative (less than 0)
• 26: positive (greater than 0)

4. Count and calculate

• Positive numbers: 1 (just the number 26)
• Total numbers: 3
• Probability = \(\frac{1}{3}\)

Answer: B. \(\frac{1}{3}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse the definition of positive numbers, thinking that "positive" means "large" rather than "greater than zero."

Some students might count -9 as positive because it's "more positive" than -11, or they might think that any number that isn't extremely negative counts as positive. This leads them to incorrectly count 2 positive numbers instead of 1.

This may lead them to select Choice C (\(\frac{2}{3}\)).

Second Most Common Error:

Conceptual confusion about probability: Students might understand which numbers are positive but then calculate probability incorrectly.

They might think probability means "how many are NOT positive" instead of "how many ARE positive," leading them to calculate \(\frac{2}{3}\) (the fraction that are negative) rather than \(\frac{1}{3}\) (the fraction that are positive).

This may lead them to select Choice C (\(\frac{2}{3}\)).

The Bottom Line:

This problem tests whether students truly understand that positive numbers are only those greater than zero, and whether they can correctly apply the basic probability formula without getting confused about what they're counting.