There are 20 buttons in a bag: 8 white buttons, 2 orange buttons, and 10 brown buttons. If one of...

1. TRANSLATE the problem information

• Given information:
  • Total buttons in bag: 20
  • White buttons: 8
  • Orange buttons: 2
  • Brown buttons: 10
  • Need to find: probability of selecting a white button at random

2. INFER the approach needed

• This is asking for a basic probability
• Since we want a white button, the "favorable outcome" is selecting a white button
• Use the probability formula: \(\mathrm{P(event)} = \frac{\mathrm{favorable\ outcomes}}{\mathrm{total\ outcomes}}\)

3. Apply the probability formula

• \(\mathrm{P(white\ button)} = \frac{\mathrm{Number\ of\ white\ buttons}}{\mathrm{Total\ number\ of\ buttons}}\)
• \(\mathrm{P(white\ button)} = \frac{8}{20}\)

Answer: B. 8/20

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread which color they're looking for or confuse the numbers given in the problem.

For example, they might focus on the non-white buttons (orange + brown = 2 + 10 = 12) and think the probability should be \(\frac{12}{20}\), leading them to select Choice D (\(\frac{12}{20}\)).

Second Most Common Error:

Conceptual confusion about probability setup: Students understand it's a probability problem but set up the fraction backwards, putting the total in the numerator and the favorable outcomes in the denominator.

This doesn't directly match any answer choice, which leads to confusion and guessing among the available options.

The Bottom Line:

This problem tests whether students can correctly identify the relevant information from a word problem and apply the most basic probability formula. The key is carefully reading what color button the problem is asking about.