Coin sets the number of dice rolls

MediumProbability Conditional Probability & Expectation~5m

Flip a fair coin until the first head; if it lands on flip $n$ , then roll a fair $6$ -sided die $n$ times. What is the probability that the value $1$ appears among those die rolls?

Show hints (2)+

Given $n$ rolls, $\mathbb{P}(\text{no }1)=(5/6)^n$ . Average over $n$ with weight $(1/2)^n$ .
The sum is geometric in $5/12$ . Don't just use the mean $n=2$ .

Answer

Reveal answer →

0.2857 (± 0.001)

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 free Unlock solutions

Asked at: Jane Street, Akuna Capital

Coin sets the number of dice rolls

Answer

Related questions