Two dice whose sum is at least their product

Question

Two fair dice are thrown. Find the probability that the total of the two faces is greater than or equal to their product.

Short answer

$\tfrac13$ . $x+y\ge xy$ is the same as $(x-1)(y-1)\le1$ . That holds whenever either die shows 1 ( $11$ outcomes) or for $(2,2)$ , giving $12$ of $36$ outcomes.

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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