I have two bags. bag 1 contains 1010 blue marbles, while bag 2 contains 1515 blue marbles. i pick one of the bags at random, and throw 66 red marbles in it. then i shake the bag and choose 55 marbles (without replacement) at random from the bag. if there are exactly 22 red marbles among the 55 chosen marbles, what is the probability that i have chosen bag 1
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