  There are four not transparent bags on the table in front of you. One of the bags has three red marbles, the second bag has two red and one blue marbles, the third bag has one red and two blue marbles, and the last has three blue marbles. If you randomly select one marble from a randomly selected bag and noticed that it is a red marble, what is the probability that your 2nd randomly selected marble from the same bag is blue? If you randomly select two marbles from a randomly selected bag and noticed that you have one red and one blue marbles in hand, what is the probability that the other marble from the same bag is blue?

Question

There are four not transparent bags on the table in front of you. One of the bags has three red marbles, the second bag has two red and one blue marbles, the third bag has one red and two blue marbles, and the last has three blue marbles.
If you randomly select one marble from a randomly selected bag and noticed that it is a red marble, what is the probability that your 2nd randomly selected marble from the same bag is blue?
If you randomly select two marbles from a randomly selected bag and noticed that you have one red and one blue marbles in hand, what is the probability that the other marble from the same bag is blue?

Step 1

Four bags contain:

The first bag contains three red marbles, the second bag has two red and one blue marbles, the third bag has one red and two blue marbles, the last bag has three blue marbles.

Step 2

Computation of the probability that the 2nd randomly selected marble from the randomly selected bag is blue:

The first randomly selected marble is red. Since there is no red balls in the last bag, it is clear that the las...

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