The fractions for both the first and second draws (A and B) from the bag are the same, with the probability of drawing a green marble being 7/11 and the probability of drawing a purple marble being 4/11.
To solve this problem, we must calculate the probabilities of drawing green and purple marbles from a bag that contains 7 green marbles and 4 purple marbles, given that we are replacing the marbles after each draw.
For the first marble (A), the probability of drawing a green marble is 7/11 since there are 7 green marbles out of a total of 11. Similarly, the probability of drawing a purple marble is 4/11 as there are 4 purple marbles out of 11.
Since the marble is replaced after the draw, the probabilities remain the same for the second marble (B). Therefore, the probability of drawing a green marble again is 7/11, and the probability of drawing a purple marble remains 4/11.
So, the fractions that should go in the boxes marked A and B are:
First marble (A): Green - 7/11, Purple - 4/11
Second marble (B): Green - 7/11, Purple - 4/11
These are the simplest forms of the fractions representing the probabilities of drawing each color marble from the bag at each draw.