Loaded Dice

You have a pair of fair dice and a pair of loaded dice. But you forgot which pair is which. You do remember that when you bought the loaded dice, the company that makes them claimed the dice would land on a sum of 7 approximately 1/3 of the time.

  1. You choose one of the pairs at random and roll it once. You get a sum of 7. What is the likelihood that you picked the loaded dice?
  2. You choose one of the pairs at random and roll the pair three times. You get exactly one sum of 7. What is the likelihood that you picked the loaded dice?

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