Day 1 · Even Before Odd¶
Edited by Sophia
| Study record | Value |
|---|---|
| Question | 1 of 4 |
| Topic | Probability |
| Difficulty | Easy |
| Attempts | 1 |
| Mastery (Notion notation) | ❚ |
| Latest attempt | October 22, 2026 |
| Source | OpenQuant: Even Before Odd |
Problem¶
Suppose you roll a fair 6-sided die until you've seen all 6 faces. What is the probability you won't see an odd numbered face until you have seen all even numbered faces?
Solution¶
The key insight is that repeated rolls don't matter—we only need to track the order of the first appearance of each distinct face. By symmetry, all \(6!\) permutations of the 6 faces appearing for the first time are equally likely. The problem requires that all three even faces appear before any odd face shows up. That means the first 3 unique faces must be even, and the remaining 3 must be odd. There are \(3!\) ways to order the even numbers and \(3!\) ways to order the odd numbers, giving \(3! \times 3!\) valid sequences. Therefore, the probability is: 1/20.