The Collector

What this coupon-collector problem tests

This is a classic easy-to-medium difficulty probability question that appears frequently in quant and data-science interviews. It tests whether you can model a sequential process, set up a system of expectations, and apply linearity of expectation to avoid heavy combinatorial computation.

The core skill is recognizing that the problem decomposes into stages: each time you acquire a new face for the first time, you're in a new "state." By reasoning about the probability of reaching each state and the expected number of rolls required to leave it, you can build up the total expected value systematically. The elegance of the solution comes from avoiding the temptation to enumerate all possible sequences.

• Linearity of expectation
• Conditional expectation and state-based reasoning
• Geometric distributions (waiting for a rare event)