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.(1 point)
The probability of Lana randomly choosing a blue marble is 5/15 because there are 5 blue marbles out of a total of 15 marbles.
Since she replaces the blue marble before choosing again, the total number of marbles remains the same at 15.
The probability of Lana choosing a purple marble is 2/15 because there are 2 purple marbles out of a total of 15 marbles.
Therefore, the probability of Lana first choosing a blue marble and then choosing a purple marble is:
(5/15) * (2/15) = 10/225 = 2/45
So, the probability that she randomly chooses a blue marble, replaces it, and then chooses a purple marble is 2/45.