A jar contains 4 red marbles, 3 white marbles, and 8 blue marbles. Two marbles are randomly selected from the jar with replacement. Find the following probabilities. Leave your answer as a reduced fraction. A red marble and then a blue marble is randomly selected. A white marble and then a red marble is randomly selected.

To solve this problem, we need to understand that "with replacement" means after selecting a marble, it is put back into the jar before the next marble is selected. This means the total number of marbles in the jar remains the same for each selection.

The total number of marbles in the jar is 4 red + 3 white + 8 blue = 15 marbles.

1. A red marble and then a blue marble is randomly selected.

The probability of selecting a red marble first is 4/15 (4 red marbles out of 15 total marbles). Since we are replacing the marble, the probability of selecting a blue marble next is 8/15 (8 blue marbles out of 15 total marbles).

To find the probability of both events happening, we multiply the probabilities together. So, the probability of selecting a red marble and then a blue marble is (4/15) * (8/15) = 32/225.

2. A white marble and then a red marble is randomly selected.

The probability of selecting a white marble first is 3/15 (3 white marbles out of 15 total marbles). The probability of selecting a red marble next is 4/15 (4 red marbles out of 15 total marbles).

So, the probability of selecting a white marble and then a red marble is (3/15) * (4/15) = 12/225 = 4/75 (after reducing the fraction).

So, the probability of selecting a red marble and then a blue marble is 32/225, and the probability of selecting a white marble and then a red marble is 4/75.