A sum of four before a sum of two

Two fair 66-sided dice are rolled repeatedly. What is the probability that a sum of 44 occurs before a sum of 22?

Show hints (2)+
  1. Only rolls summing to 22 or 44 matter. Find each one's per-roll probability.
  2. The race winner is P(4)/(P(4)+P(2))=3/(3+1)\mathbb{P}(4)/(\mathbb{P}(4)+\mathbb{P}(2)) = 3/(3+1).

Answer

Reveal answer →

0.75

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: Optiver, Akuna Capital

Related questions