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I have two bags. Bag 1 contains 10 blue marbles, while Bag 2 contains 15 blue marbles. I pick one of the bags at random, and throw 6 red marbles in it. Then I shake the bag and choose 5 marbles (without replacement) at random from the bag. If there are exactly 2 red marbles among the 5 chosen marbles, what is the probability that I have chosen Bag 1?

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ignacioorme

Answer:

The probability of choosing bag 1 is 0,0412

Step-by-step explanation:

As the question emphasizes the probability of bag one, it is that we consider only this one. Bag 1 contains 10 blue marbles and 6 red marbles are added, in total 16 marbles. From this bag 1 extract 3 blue and 2 red marbles, without repetition. In probability it is expressed:

P (Bag₁) = 10/16 * * 9/15 * 8/14 * 6/13 * 5/12 = 0,0412

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