A bag contains a total of 12 marbles, and each marble is either green or white. Of the marbles in...

1. TRANSLATE the problem information

• Given information:
  • Total marbles: 12
  • Green marbles: 8
  • Each marble is either green or white
  • Find: P(selecting white marble)

• This tells us we need to use the probability formula: \(\mathrm{P(event)} = \frac{\text{favorable outcomes}}{\text{total outcomes}}\)

2. INFER what information we're missing

• We know there are 8 green marbles out of 12 total
• Since each marble is either green OR white, the remaining marbles must be white
• White marbles = \(12 - 8 = 4\) marbles

3. Apply the probability formula

• \(\mathrm{P(white\ marble)} = \frac{\text{Number of white marbles}}{\text{Total marbles}}\)
• \(\mathrm{P(white\ marble)} = \frac{4}{12}\)

4. SIMPLIFY the fraction

• \(\frac{4}{12} = \frac{1}{3}\)

Answer: B) 1/3

Acceptable forms: 1/3, 0.333..., or approximately 0.33

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misunderstand what "probability of white" means and instead calculate the probability of green marbles.

They see 8 green marbles out of 12 and think: \(\mathrm{P} = \frac{8}{12} = \frac{2}{3}\)

This leads them to select Choice C (2/3)

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly find that \(\mathrm{P(white)} = \frac{4}{12}\) but fail to reduce the fraction to lowest terms.

Since 4/12 doesn't appear as an answer choice, this causes confusion and they may guess or incorrectly try to match it with 1/4.

This may lead them to select Choice A (1/4) or causes them to get stuck and guess.

The Bottom Line:

This problem tests whether students can correctly identify what they're looking for (white marbles, not green marbles) and remember that probability problems often require finding missing information through logical reasoning rather than just using given numbers directly.