since you are replacing the marble, the second draw is not affected by anything you did before.
so Prob(red, then blue) = (8/43)(12/43)
= 96/1849
20/43
40/43
20/1849
96/1849
so Prob(red, then blue) = (8/43)(12/43)
= 96/1849
9/20
reiny is wrong
Step 1: Determine the probability of selecting a red marble.
The bag contains a total of 5 + 8 + 11 + 7 + 12 = 43 marbles.
The number of red marbles is 8, so the probability of selecting a red marble on the first draw is 8/43.
Step 2: Determine the probability of selecting a blue marble.
After replacing the red marble, the bag still contains a total of 43 marbles.
The number of blue marbles is 12, so the probability of selecting a blue marble on the second draw is 12/43.
Step 3: Calculate the probability of both events occurring.
Since the events of choosing a red marble and then a blue marble are independent, we can multiply the probabilities together.
P(red then blue) = (8/43) * (12/43) = 96/1849.
The correct answer is 96/1849.