Dice total of 4 showing up before a 2

Question

Jed keeps rolling a pair of fair six-sided dice. What is the probability that he rolls a total of $4$ before he rolls a total of $2$ ?

Short answer

$\tfrac34$ . Rolls with any other total are irrelevant. A total of $4$ arises in $3$ ways out of $36$ and a total of $2$ in $1$ way, so the first relevant roll is a $4$ with probability $\tfrac{3}{3+1}$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Counting and Combinatorics
Expectation, Mean, and Variance

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