The fraction that should go in Box A is 9/13,the fraction that should go in Box B is 4/13.
To determine the fractions that should go in the boxes marked A and B, we need to consider the given information.
We know that there are 13 marbles in total, with 9 of them being yellow and the rest being purple. This means that there are 4 purple marbles in the bag.
For Box A, we need to find the probability of picking a yellow marble on the first draw. Since there are 9 yellow marbles and a total of 13 marbles, the probability is:
Probability of picking a yellow marble on the first draw = Number of favorable outcomes / Total number of possible outcomes
Probability of picking a yellow marble on the first draw = 9 / 13
The fraction that should go in Box A is 9/13.
For Box B, we need to find the probability of picking a purple marble on the second draw, given that a yellow marble was picked and replaced on the first draw. Since the marbles are replaced after each draw, the probability remains the same.
The probability of picking a purple marble on the second draw is the same as the probability of picking a purple marble from the original set of marbles, which is:
Probability of picking a purple marble on the second draw = Number of purple marbles / Total number of marbles
Probability of picking a purple marble on the second draw = 4 / 13
The fraction that should go in Box B is 4/13.
Box A: 9/13
Box B: 4/13