Lana has a bag of 15 marbles. There are 2 black marbles, 5 blue, 3 red, 3 green, and 2 purple. What is the probability that she randomly chooses a blue marble, replaces it, and then chooses a purple marble? Write your answer as a fraction in the simplest form.(
The probability of choosing a blue marble on the first draw is 5/15. Since the marble is replaced, Lana still has 15 marbles. The probability of choosing a purple marble on the second draw is 2/15.
Therefore, the probability of Lana randomly choosing a blue marble, replacing it, and then choosing a purple marble is (5/15) * (2/15) = 10/225 = 2/45.
So, the probability is 2/45.