A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If...

1. TRANSLATE the problem information

• Given information:
  • Total marbles: 60
  • Probability of blue marble: 0.35
• What we need to find: Number of blue marbles

2. INFER the mathematical relationship

• Key insight: If we know the probability and total count, we can find the number of favorable outcomes
• The probability formula is: \(\mathrm{P(event)} = \frac{\mathrm{favorable\ outcomes}}{\mathrm{total\ outcomes}}\)
• Rearranging: \(\mathrm{favorable\ outcomes} = \mathrm{P(event)} \times \mathrm{total\ outcomes}\)

3. SIMPLIFY by calculating

• Number of blue marbles = \(0.35 \times 60\)
• \(0.35 \times 60 = 21\) (use calculator if needed)

Answer: A. 21

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about probability: Students might interpret 0.35 as meaning "35 marbles" directly, without understanding that probability is a ratio.

This leads them to think there are 35 blue marbles, causing them to select Choice C (35).

Second Most Common Error:

Weak INFER skill: Students calculate the correct number of blue marbles (21) but then mistakenly find the number of non-blue marbles instead.

They compute \(60 - 21 = 39\) and select Choice D (39).

The Bottom Line:

This problem tests whether students truly understand probability as a ratio rather than a direct count, and whether they can work backwards from probability to find actual quantities.