I have three bags that each contain 100 marbles: Bag 1 has 75 red and 25 blue

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I have three bags that each contain 100 marbles:

  • Bag 1 has 75 red and 25 blue marbles;
  • Bag 2 has 60 red and 40 blue marbles;
  • Bag 3 has 45 red and 55 blue marbles.

I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?

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