Nneetquant
Get started

Four fives before the first six

MediumProbabilityRandom Variables~5m

You roll a fair 66-sided die until you get your first 66. What is the probability that a 55 appears exactly four times before that first 66?

Show hints (2)+
  1. Rolls of 1,2,3,41,2,3,4 don't matter - restrict to {5,6}\{5,6\} rolls, each equally likely.
  2. Then the count of 55s before the first 66 is geometric: P(k)=(1/2)k+1\mathbb{P}(k)=(1/2)^{k+1}.

Answer

Reveal answer →

0.03125 (± 0.0005)

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

Practise freeUnlock solutions

Asked at: Jane Street, Akuna Capital

Related questions