Jellybean Jar I

What this sampling-without-replacement probability question tests

This is an easy probability question that appears frequently in quant interviews to check whether candidates can reason about sequential sampling without replacement. The problem requires setting up conditional probabilities as items are drawn from a finite pool, then multiplying them together to find the joint probability of a specific sequence.

The key insight is recognizing that each draw changes the composition of the remaining pool, so the probability of each subsequent event depends on what was already drawn. Candidates typically enumerate the four draws in order, compute the marginal probability at each step, and then multiply. Simplifying the final fraction tests whether you can identify common factors and reduce to lowest terms.

• Conditional probability and the multiplication rule
• How sampling without replacement affects successive probabilities
• Fraction arithmetic and GCD reduction