Collect them All, Again!

What this coupon collector problem teaches

This is an easy-to-medium probability question that tests your understanding of the coupon collector problem, a classic framework in probability and statistics. It's popular in quant interviews because it rewards clear thinking about expected value and conditional probability over computational brute force.

The core challenge is to recognize that collecting the final items becomes progressively harder as you already own most of the set. Rather than assume a uniform average, you need to account for the changing probability of drawing a new figure at each stage. This is a canonical application of linearity of expectation, where you decompose the problem into stages and sum the expected cost of each.

• Geometric distribution and memorylessness
• Linearity of expectation over dependent events
• Harmonic series approximations