Probability of a language chain

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There are 10 languages spoken at a conference, and 10 translators. Each translator can translate between exactly 2 of the 10 languages, with the 2 languages spoken by any translator being random and independent. Some translators may speak the same pair of languages. Using all 10 translators, what is the probability of being able to translate (directly or indirectly) between given languages A and B?