The Heavy Crate

What this probability question tests

This is an easy probability problem that measures how quickly you can set up a counting argument under a symmetry constraint. It appears frequently in quant interviews because it rewards clear thinking about conditional probability and sample spaces over computation.

To solve problems like this, candidates typically identify all possible partitions of the crates, determine which satisfy the condition, and compute the ratio. The key insight is recognizing what information matters and what simplifies the calculation. Firms value candidates who can articulate why certain outcomes are equivalent and use that structure to avoid unnecessary casework.

• Counting outcomes in equally likely partitions
• Conditional probability given a fixed element
• Symmetry and combinatorial reduction