Six showing on a pair of dice that total eight

Question

Two fair dice are thrown and their faces add up to $8$ . Given this, what is the probability that at least one of the dice shows a $6$ ?

Short answer

$\tfrac25$ . The ordered outcomes with total $8$ are $(2,6),(3,5),(4,4),(5,3),(6,2)$ , all equally likely. Exactly two of these five contain a $6$ .

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

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Counting and Combinatorics
Expectation, Mean, and Variance

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