Of the 8 planets in our solar system, 4 are considered rocky. If a student randomly selects 1 of those...

1. TRANSLATE the problem information

• Given information:
  • Total number of planets: 8
  • Number of rocky planets: 4
  • We need the probability of randomly selecting a rocky planet

2. INFER the approach needed

• This is a basic probability problem
• We need to use: \(\mathrm{Probability = \frac{favorable\:outcomes}{total\:outcomes}}\)
• Favorable outcomes = rocky planets (4)
• Total outcomes = all planets (8)

3. SIMPLIFY to get the final answer

• Probability = \(\mathrm{\frac{4}{8} = \frac{1}{2}}\)

Answer: C. \(\mathrm{\frac{1}{2}}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students reverse the probability formula and divide total outcomes by favorable outcomes instead of favorable by total.

They calculate \(\mathrm{8 \div 4 = 2}\), thinking "there are 8 planets for every 4 rocky ones."

This leads them to select Choice D (2).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misread or misunderstand the numbers in the problem.

They might think only 1 planet is rocky (selecting \(\mathrm{\frac{1}{8}}\)) or only 2 planets are rocky (selecting \(\mathrm{\frac{2}{8} = \frac{1}{4}}\)), not carefully processing that "4 are considered rocky."

This may lead them to select Choice A (\(\mathrm{\frac{1}{8}}\)) or Choice B (\(\mathrm{\frac{1}{4}}\)).

The Bottom Line:

This problem tests whether students can correctly set up a basic probability fraction. The key insight is that probability is always "what you want" divided by "what's possible" - never the other way around.