Total of five appearing before a total of two

Question

You repeatedly throw a pair of fair dice. What is the probability that a total of $5$ turns up before a total of $2$ ?

Short answer

$4/5$ . Only throws totalling $5$ ( $4$ outcomes) or $2$ ( $1$ outcome) matter. The first of these is a $5$ with probability $\tfrac{4}{4+1}=\tfrac45$ .

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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