Each face of a fair 14-sided die is labeled with a number from 1 through 14, with a different number...

1. TRANSLATE the problem information

• Given information:
  • Fair 14-sided die (each outcome equally likely)
  • Each face has a different number from 1 to 14
  • We want the probability of rolling a 2

• What this tells us:
  • Total possible outcomes: 14
  • Favorable outcomes: 1 (only one face shows "2")

2. INFER the approach

• This is a basic probability problem requiring the fundamental probability formula
• We need to identify favorable outcomes and divide by total outcomes

3. Apply the probability formula

\(\mathrm{P(rolling\, a\, 2)} = \frac{\mathrm{favorable\, outcomes}}{\mathrm{total\, outcomes}}\)

\(\mathrm{P(rolling\, a\, 2)} = \frac{1}{14}\)

Answer: A. 1/14

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the question and calculate the probability of NOT rolling a 2 instead of rolling a 2.

They correctly identify that there are 13 faces that don't show "2" and 14 total faces, leading them to calculate \(\frac{13}{14}\). This misreading of what the question asks for is surprisingly common in probability problems.

This may lead them to select Choice D (\(\frac{13}{14}\)).

The Bottom Line:

This problem tests whether students can carefully read what event they're supposed to find the probability for. The mathematics is straightforward, but attention to detail in interpreting the question is crucial.