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 is 5/15 = 1/3 because there are 5 blue marbles out of a total of 15 marbles.
Since Lana replaces the blue marble before choosing another one, the probability of choosing a purple marble is 2/15, because there are 2 purple marbles out of a total of 15 marbles.
To find the probability of both events happening together (choosing a blue marble and then a purple marble), we multiply the probabilities:
(1/3) * (2/15) = 2/45
Therefore, the probability that Lana randomly chooses a blue marble and then a purple marble is 2/45.