A bag contains 8 blue marbles 5 red marbles and 2 orange marbles, Carolina picks a marble from the bag at random and returns it to the bag and makes a second random selection. What is the probability that two blue marbles were selected

Initial total number of marbles: 8 + 5 + 2 = 15

Initial number of blue marbles: 8

First pick:

p (blue marble) = 8/15

Since the marble from the first pick is returned to the bag, the bag still contains 8 blue marbles and a total of 15 marbles.

Second pick:

p (blue marble) = 8/15

Overall:

p (blue marble followed by blue marble) =

= p (blue marble) * p (blue marble)

= 8/15 * 8/15

= 64/225