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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.