Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
A cube painted red on all sides is cut into 125 equal small cubes. A small cube when picked is found to show red color on one of its faces. The probability that two more faces also show red color is :
$\frac{4}{75}$
$\frac{4}{49}$
$\frac{1}{8}$
$\frac{8}{125}$
Step-by-Step Solution
Key Concept: Use conditional probability: restrict sample space to cases where at least one cube is red, then count favorable outcomes.
This is conditional probability. Total cases with at least one red cube: $125 - 27 = 98$. Among these, cubes painted on exactly three sides: 8. The conditional probability is $ rac{8}{98} = rac{4}{49}$.
Correct Answer: 2