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Algebra Difficulty 2.0 Junior Prove it Canada

Two fair dice, each having six faces numbered $1$ to $6$ , are thrown. What is the probability that the product of the two numbers on the top faces is divisible by $5$ ?

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.